Thorsten Rheinländer Memorial Colloquium (TRMC 2026)
Vienna, Monday, October 12, 2026
https://fam.tuwien.ac.at/trmc2026/

Jonas Ingmanns, Institute of Science and Technology Austria (ISTA)
17:00-18:00, Freihaus building, lecture hall 8
Marktkonsistente Bewertung von Verbindlichkeiten in der Krankenversicherung hinsichtlich Inflation
Veranstaltungsreihe "Actuarial Modelling Club"

Bartosz Gaweda, Milliman
17:00-18:00, Freihaus building, lecture hall 8
Accidents that never happened: Generative AI and fraud in motor insurance
Veranstaltungsreihe "Actuarial Modelling Club"

Dietmar Hareter, Jonas Hirz, Andreas Magenschab, Christof Peternell, Fabian Pribahsnik, Aktuarvereinigung Österreichs (AVÖ)
17:00-18:00, Freihaus building, lecture hall 8
Wenn Modelle denken zu denken: Warum es Aktuare braucht
Veranstaltungsreihe "Actuarial Modelling Club"

Marcel Smith, MavenBlue
17:00-18:00, Freihaus building, lecture hall 8
Spread Risk in Balance Sheet Valuation and Projection: Options and Guarantees
Veranstaltungsreihe "Actuarial Modelling Club"

Noa Zamstein, Senior Data Science Researcher, Earnix
17:00-18:00, Freihaus building, lecture hall 1
Advancing Actuarial Science: Leveraging Synthetic Data for Privacy-Preserving Modeling
Veranstaltungsreihe "Actuarial Modelling Club"

Manuel Lang (UNIQA Österreich Versicherungen AG) und Tobias Preinerstorfer (B&W Deloitte GmbH)
17:00-18:00, Freihaus building, lecture hall 8
Modellierung in der Krankenversicherung - Herausforderungen und Lösungsansätze
Veranstaltungsreihe "Actuarial Modelling Club"

Guido Berendes (Deutsche Rückversicherung AG)
17:00-18:00, online via MS-Teams
Right to be forgotten (RTBF) - aktueller Stand und Auswirkungen
Veranstaltungsreihe "Actuarial Modelling Club"

 
Vienna Congress on Mathematical Finance (VCMF 2025)
Vienna, Wed.-Fri., July 9-11, 2025
https://fam.tuwien.ac.at/vcmf2025/

Kristof Wiedermann (FAM @ TU Wien)
10:30, conference room of the Deanery (Freihaus, 9th floor, green area - elevator only until 8th floor, then starecase)
or online via Zoom (join Zoom meeting, ID: 637 6686 8808, PW: A7JJ4vkM)
Stochastic Volterra Integral Equations: Central Limit Theorems, Non-Markovianity and Markovian Lifting
(Public PhD Thesis Defense) (close abstract)

In this work, we study stochastic Volterra integral equations (SVIEs) of convolution type, frameworks for Hilbert space-valued Markovian lifts of the latter, small-time limit theorems for both classes of processes and four independent proof concepts for verifying that solutions to sufficiently non-degenerate SVIEs cannot possess the Markov property. While the latter appears as a unanimously agreed fact in the literature, so far a rigorous mathematical proof thereof has been absent.
 
In the first part of the thesis, we prove a small-time central limit theorem (CLT) for the finite-dimensional distributions of sufficiently smooth transformations of solutions to stochastic Volterra integral equations as well as its extension to a functional CLT. Here we focus on kernels with small-time power law asymptotics and coefficients satisfying linear growth and Hölder conditions. Moreover, as an application of the obtained functional CLT in the context of rough volatility models, we derive asymptotic pricing formulae for digital calls on the realized variance in three different regimes showcasing high robustness with regard to the parameters of the underlying volatility process. The results hold in particular for the rough Heston model.
 
Furthermore, we introduce a framework of Hilbert space-valued Markovian lifts for SVIEs which is particularly suited for scalar completely monotone kernels whose Bernstein measures fulfill a mild moment condition. We proceed by deriving a corresponding small-time CLT and a functional CLT also for transformations of the Markovian lift under suitable continuous linear functionals. As a special case, this contains in particular the above CLT for the Volterra process itself, provided that a certain projection operator is applicable.
 
As an application of the CLT framework, the first approach presented for proving the failure of the time-homogeneous Markov property for stochastic Volterra integral equations unveils a connection with the non-Markovianity of the Gaussian limit process obtained in the above CLT. In particular, we show that once this limit process is not a Markov process, also the original Volterra process cannot possess the time-homogeneous Markov property. Except for the generally Markovian SDE case, our result contains SVIEs with Riemann-Liouville and gamma kernels for the full range of the Hurst parameter.
Furthermore, our second and third method are specifically designed for SVIEs with affine drifts. As for these processes there exist semi-explicit formulae for expectations and conditional expectations, we can show by solving certain integro-functional equations that an SVIE solution with an exponential or constant initial curve which fulfills the time-homogeneous Markov property necessarily has to possess a kernel of the same type. When the drift vanishes, analogous results are obtained under structural assumptions on the diffusion coefficient. Moreover, based on the semi-explicit formula for conditional expectations, we show that by the non-measurability of a certain path functional, the Volterra square-root process cannot even possess the time-inhomogeneous Markov property.
 
Finally, in our most universal result on the failure of the time-inhomogeneous Markov property, we consider general d-dimensional SVIEs with matrix-valued Volterra kernels and a potentially random initial curve which is measurable with respect to the information provided at time zero. In an abstract framework for Markovian lifts of these SVIEs onto a suitable separable Hilbert space, which includes the previously introduced lift as a special case, we prove the failure of the Markov property once there exists an admissible, suitably non-degenerate second Volterra kernel that can be obtained by perturbations of the original Volterra kernel, while similar approximations have to converge also for the initial curve, if it is random. Such perturbations are usually realized via applications of appropriate bounded linear operators to the corresponding lift. In particular, this framework covers the classes of completely monotone and absolutely continuous kernels which fulfill certain technical integrability conditions required for constructing the corresponding lift. For example, our results include d-dimensional SVIEs with (diagonal) rough, regular and shift-regularized Riemann-Liouville and gamma kernels and Hölder continuous drift and diffusion coefficients.
 

Onnen Siems, Carina Götzen (Meyerthole Siems Kohlruss GmbH)
17:00-18:00, Freihaus building, lecture hall 8
Rain Chaser - Modellierung des Oberflächenwasserabflusses bei Starkregenereignissen
Veranstaltungsreihe "Actuarial Modelling Club"

Alexander Meiksner, Thomas Hochreiter, Michael Reichard (arithmetica Consulting GmbH)
17:00-18:00, Freihaus building, lecture hall 8
Risikotransfer und Optimierung der Rückversicherung
Veranstaltungsreihe "Actuarial Modelling Club"

Michael Leitschkis (Athora Group, DE)
17:00-18:00, Freihaus building, lecture hall 8
Machine Learning-Anwendungen von Proxy Modelling bis Klimawandel
Veranstaltungsreihe "Actuarial Modelling Club"

Praxis der Finanz- und Versicherungsmathematik 2024
(Mathematiker_innen in der Finanz- und Versicherungsbranche)
TU Wien, Anmeldung erforderlich!

Praxis der Finanz- und Versicherungsmathematik 2024
(Berufsständisches Seminar)
TU Wien, Anmeldung erforderlich!

Eckhard Platen (University of Technology Sydney)
17:00-18:00, Freihaus building, lecture hall 8
Anwendung des Benchmark Ansatzes für die Altersversorgung
Veranstaltungsreihe "Actuarial Modelling Club"

Florian Nuding (Wüstenrot), Bartosz Gaweda (Milliman), Jan Küthe (Akur8)
16:30-18:00, Freihaus building, lecture hall 8
Cutting-edge in Pricing: Penalized Regression, Market Price Insights, and Practical Lessons
Veranstaltungsreihe "Actuarial Modelling Club"

DI Lukas Ludwig (FWU AG)
17:00-18:00, Freihaus building, lecture hall 8
POG - Der »neue« Produktentwicklungsstandard
Veranstaltungsreihe "Actuarial Modelling Club"

Sven Ebert (Flossbach von Storch Research Institute, DE)
17:00-18:00, Freihaus building, lecture hall 8
Aktuarielle Betrachtungen zu Demographie und Inflation
Veranstaltungsreihe "Actuarial Modelling Club"

Lorenz Meinl & Jung-Geun Seok (B&W Deloitte GmbH)
17:00-18:00, Freihaus building, lecture hall 8
Marktpricing - effiziente Preisstrategien und Dynamic Pricing
Veranstaltungsreihe "Actuarial Modelling Club"

Andrea Rauter und Daniel Thompson (B&W Deloitte GmbH)
17:00-18:00, Freihaus building, lecture hall 8
IFRS 17 Veröffentlichungen - Q2 2023 Disclosures
Veranstaltungsreihe "Actuarial Modelling Club"

Stefan Gerhold (FAM @ TU Wien)
18:00-19:00, Nöbauer Hörsaal 8 and online
Die Mathematik der Finanzmärkte
TUForMath

Matthias Widman (d-fine Austria GmbH)
17:00-18:00, Freihaus building, lecture hall 8
Aktivseitige, risikoneutrale Modellierung in einem Versicherungsunternehmen
Veranstaltungsreihe "Actuarial Modelling Club"

Gabriele Hollmann (SCOR)
17:00-18:00, Freihaus building, lecture hall 8
Behavioral Science und Lebensversicherung
Veranstaltungsreihe "Actuarial Modelling Club"

Alexander Bontjes van Beek (EY)
17:00-18:00, Valida, Mooslackengasse 12, 1190 Wien
Abhängigkeitsmodellierung operationeller Risiken - ein Bernstein-Copula Ansatz
Veranstaltungsreihe "Actuarial Modelling Club"

Praxis der Finanz- und Versicherungsmathematik 2022
(Mathematiker_innen in der Finanz- und Versicherungsbranche)
TU Wien, Anmeldung erforderlich!

Praxis der Finanz- und Versicherungsmathematik 2022
(Berufsständisches Seminar)
TU Wien, Anmeldung erforderlich!

Alexander Meiksner (arithmetica Consulting GmbH)
17:00-18:00, Freihaus building, lecture hall 5
Aktuellste Entwicklungen zur Methodik der EIOPA-Zinskurve
Veranstaltungsreihe "Actuarial Modelling Club"

Ulrike Ebner (Wiener Städtische Versicherung - Vienna Insurance Group)
16:30-17:30, Freihaus building, lecture hall 8
Aktuarielle Projektionsmodelle - mehr als nur ein Spielzeug für Aktuare
Veranstaltungsreihe "Actuarial Modelling Club"

Carmen Boado-Penas (University of Liverpool)
17:00-18:00, Freihaus building, lecture hall 8
Automatic balancing mechanisms for state pensions: Past, present and future
Veranstaltungsreihe "Actuarial Modelling Club"

Julia Eisenberg (FAM @ TU Wien)
18:00-19:00, Nöbauer Hörsaal 8 and online
Brauchen Versicherungen mehr Mathematik als die Grundrechenarten?
TUForMath

Christoph Gerstenecker (FAM @ TU Wien)
10:15, lecture hall Freihaus Hörsaal 7 (Freihaus, Wiedner Hauptstr. 8, yellow area, 2nd floor)
Large Deviations and Stochastic Volterra Equations (close abstract)

This thesis consists of three parts, all of which are related to large deviations theory. In the second and third part, stochastic Volterra integral equations play an important role. Stochastic Volterra equations are essential when it comes to rough volatility models, because a natural way of introducing roughness in a (classic) stochastic volatility model is to add a fractional (weakly singular) kernel to the integrand coefficient functions of an ordinary Ito diffusion. Large deviations results help, in a variety of situations, to establish asymptotic results. These can be used to develop asymptotic results for all kind of objects in the area of Financial Mathematics. These results can e.g. be used for investigating the qualitative behavior of these objects in a special situation or to develop fast calibration schemes.
Chapter 1: "Preliminaries and some well-known results", presents some results from the literature and introduces notions and results from large deviations theory.
Chapter 2: "Large deviations related to the law of the iterated logarithm for Ito diffusions", is based on paper that was joint work with Stefan Gerhold, published in the journal "Electronic Communications in Probability". This work is a pure mathematics topic and does not provide applications in Finance. In this chapter, we establish a large deviations principle for the supremum of a scaled Ito diffusion. When a Brownian motion is scaled according to the law of the iterated logarithm, its supremum converges to one as time tends to zero. Upper large deviations of the supremum process can be quantified by writing the problem in terms of hitting times and applying a result of Strassen (1967) on hitting time densities. We extend this to a small-time large deviations principle for the supremum of scaled Ito diffusions, using as our main tool a refinement of Strassen's result due to Lerche (1986).
Chapter 3: "Large deviations for fractional volatility models with non-Gaussian volatility driver", is based on a paper that was joint work with Stefan Gerhold and Archil Gulisashvili, published in the journal "Stochastic Processes and their Applications". In this chapter, we study non-Gaussian fractional stochastic volatility models. The volatility in such a model is described by a positive function of a stochastic process that is a fractional transform of the solution to an SDE satisfying the Yamada-Watanabe condition. Such models are generalizations of a fractional version of the Heston model considered in Bäuerle and Desmettre (2020). We establish sample path small-noise large deviation principles for the log-price process in a non-Gaussian model. We also illustrate how to compute the second order Taylor expansion of the rate function, in a simplified example.
Chapter 4: "Rough 3/2 -- A truncated ansatz", is based on a joint working paper with Stefan Gerhold. In this chapter, we come up with a rough variant of the well-known 3/2 model. The coefficient functions of the underlying stochastic Volterra integral equation (SVE) are truncated in an appropriate manner to ensure existence of the solution. The computations for showing existence according to Zhang (2010) are shown in detail such that they can easily be followed. With the help of Jacquier and Pannier (2020) we establish sample path small-noise and small-time large deviations for the instantaneous variance and the log-price process. For some of these we also get moderate deviation principles. Then, we present some applications of these large deviations results. Also a simple implementation using a naive Euler approach for the simulation of sample paths is given at the end of this chapter.
 
German:
Die vorliegende Arbeit besteht aus drei Teilen, die Resultate der Large Deviations Theory benutzen. In den letzten beiden Teilen spielen auch stochastische Volterra Integralgleichungen eine wichtige Rolle. Diese sind essenziell, wenn man in klassischen stochastischen Volatilitätsmodellen einen fraktionellen Kern in die Gleichung für die Instantaneous Variance einführen möchte, um eine "rough" Version dieses Modells zu erzeugen. Large deviations werden oft benutzt, um in einer Vielzahl von Situation asymptotische Resultate herzuleiten. Diese Resultate sind besonders in der Finanzmathematik gefragt, sei es um finanzmathematische Größen, wie etwa Optionspreise, Implied Volatility, etc., qualitativ zu beurteilen oder auch z.B. für Fast Calibration Schemes.
Kapitel 1: "Preliminaries and some well-known results", präsentiert einige aus der Literatur bekannte Resultate, die wir im weiteren auch verwenden werden. Auch die für diese Arbeit relevanten Definitionen und Resultate aus der Large Deviations Theory werden hier überblicksmäßig gezeigt.
Kapitel 2: "Large deviations related to the law of the iterated logarithm for Ito diffusions", basiert auf einem Paper zusammen mit Stefan Gerhold, das im Journal "Electronic Communications in Probability" publiziert wurde. In diesem Teil der Arbeit zeigen wir ein Large Deviations Principle für das Supremum einer skalierten Ito Diffusion. Skaliert man eine Brownsche Bewegung wie beim Gesetz des iterierten Logarithmus, dann konvergiert das Supremum davon gegen Eins wenn die Zeit gegen Null geht. Upper Large Deviations dieses Prozesses bekommt man, indem man das Problem via Trefferzeiten einer stetigen Kurve formuliert und dann Resultate für Trefferzeiten von Strassen (1967) anwendet. Wir erweitern das ganze zu einem small-time Large Deviations Principle für das Supremum einer skalierten Ito Diffusion, wobei die Hauptreferenz ein Resultat von Lerche (1986) ist, das auf Strassens Resultat aufbaut.
Kaptiel 3: "Large deviations for fractional volatility models with non-Gaussian volatility driver", basiert auf einem Paper gemeinsam mit Stefan Gerhold und Archil Gulisashvili, das im Journal "Stochastic Processes and their Applications" publiziert wurde. In diesem Kapitel betrachten wir "non-Gaussian fractional stochastic volatility models". Die Volatilität in solch einem Modell besteht aus einer positiven Funktion mit einem stochastischen Prozess als Argument. Dieser wird erzeugt durch eine fraktionelle Transformation der Lösung einer stochastischen Differentialgleichung, wobei die Yamada-Watanabe-Bedingung erfüllt sein muss. Derartige Modelle sind Verallgemeinerungen der fractional Version des Heston Modells aus Bäuerle und Desmettre (2020). Wir zeigen pfadweise Large Deviations und small-noise Large Deviations für den Log-Preis in einem solchen non-Gaussian Modell. Weiters zeigen wir in einem sehr vereinfachten Beispiel, wie man die Taylor Entwicklung zweiter Ordnung für die Rate Function dieser Large Deviations Principles berechnen könnte.
Kapitel 4: "Rough 3/2 -- A truncated ansatz", ist eine gemeinsame Arbeit mit Stefan Gerhold, die noch nicht publiziert wurde. In diesem Teil der Arbeit wird eine "rough" Variante des bekannten nicht-affinen 3/2-Modells vorgeschlagen. Die Koeffizienten(funktionen) der zugrundeliegenden stochastischen Volterra Gleichung (SVE) werden in geeigneter Weise abgeschnitten, um die Existenz einer Lösung zu sichern. Es wird gezeigt, dass unser Modell die Voraussetzungen von Zhang (2010) erfüllt. Dennoch werden die notwendigen Abschätzungen für den Existenzbeweis ausführlich gezeigt, um sie einfach nachvollziehbar zu machen. Mithilfe von Jacquier und Pannier (2020) bekommen wir, nachdem alle Voraussetzungen gezeigt wurden, pfadweise small-noise und small-time Large Deviations für die Instantaneous Variance und den Log-Preis Prozess. Für einen Teil davon bekommen wir dann auch Moderate Deviations Principles. Am Ende dieses Teils der Arbeit werden noch ein paar Anwendungsbeispiele gebracht, wie etwa Asymptotiken für Implied Volatility und Optionspreise auf Realized Variance. Weiters wird ein Implementierungsvorschlag mittels eines naiven Euler Schemes zur Simulation der Pfade präsentiert.
 

Götz Cypra and Michael Feigl (UNIQA Capital Markets GmbH)
16:30-17:30, online via Zoom
Asset-Liability-Management für Versicherungen
Veranstaltungsreihe "Actuarial Modelling Club"

Rachel Hillier (Capital Law Limited, UK)
16:30-17:30, online via Zoom
Is Parametric Insurance the answer to the Legal Challenges of Insuring Against a Pandemic?
Veranstaltungsreihe "Actuarial Modelling Club"

Daniel Wimmer (Erste Group)
16:30-17:30, online via Zoom
Modellrisiko bei der Schätzung von epidemiologischen Parametern bei Covid-19
Veranstaltungsreihe "Actuarial Modelling Club"

Walter Pöltner (Vorsitzender der Alterssicherungskommission)
16:30-17:30, online via Zoom
Die Alterssicherungskommission: Aufgabe und Funktion im Rahmen einer nachhaltigen Sozialpolitik
Veranstaltungsreihe "Actuarial Modelling Club"

Jürgen Hartinger (Kärntner Landesversicherung) sowie Mario Kasper und Sven Ebert (SCOR Global Life) und
16:30-17:30, online via Zoom
Lebensversicherung als »Datenkrake oder Gesundheitspartner«?
Veranstaltungsreihe "Actuarial Modelling Club"

Sven Jörgen (Valida Consulting GesmbH)
16:30-18:00, online via Zoom
Bewertung von Pensionsrückstellungen - ein Überblick
Veranstaltungsreihe "Actuarial Modelling Club"

Frank Schiller (MunichRe)
16:00-18:00, online via Zoom
Wie überlebt man eine Pandemie als Aktuar?
Veranstaltungsreihe "Actuarial Modelling Club"

Wolfgang Herold (Finanzmarktaufsicht - FMA)
16:30-17:30, online via Zoom
Kapitalmarkt - aktuelle Entwicklungen und ihre Bedeutung für den Versicherungsmarkt
Veranstaltungsreihe "Actuarial Modelling Club"

Michael Kinzer (Michael Kinzer Consulting) und Bernd Weber (Zürich Versicherungs-Aktiengesellschaft)
16:30, online via Zoom
Liability-2-Step - Ein Ansatz zur stochastischen Bewertung von Lebensversicherungs-Portfolios ohne Verdichtung
Veranstaltungsreihe "Actuarial Modelling Club"

Dietmar Hareter und Fabian Pribahsnik (Wiener Städtische Versicherung AG Vienna Insurance Group)
16:30, online via Zoom
Data Science im Live-Betrieb (Ein Online-Vortrag von Praktikern für Praktiker_innen)
Veranstaltungsreihe "Actuarial Modelling Club"

Praxis der Finanz- und Versicherungsmathematik 2020
(Mathematiker_innen in der Finanz- und Versicherungsbranche)
TU Wien, Anmeldung erforderlich!

Praxis der Finanz- und Versicherungsmathematik 2020
(Berufsständisches Seminar)
TU Wien, Anmeldung erforderlich!

Alexander Juschitz (B&W Deloitte)
16:30, Online via Zoom
Die Standard Formel unter Solvency 2 und die Prüfung ihrer Angemessenheit
Veranstaltungsreihe "Actuarial Modelling Club"

Sebastian Helbig und Marius Reitz (ROKOCO GmbH und ROKOCO Predictive Analytics GmbH)
16:30 - 18:00, FH 8 Nöbauer Hörsaal (Freihaus, 2. OG, gelb)
Marktkonsistenz und Solvabilitätsbewertung: Ausgewählte Aspekte
Veranstaltungsreihe "Actuarial Modelling Club"

Götz Cypra (UNIQA), Mario Hoerig (Oliver Wyman)
17:00, GM 3 Vortmann Hörsaal (Plus Energie Büro Hochhaus, 2. OG, Getreidemarkt 9)
Deep Learning Techniken im Einsatz: Anwendungen im Kontext von Economic Capital und Cash Flow Projektionsmodellen
Veranstaltungsreihe "Actuarial Modelling Club"

Florian Gach (FMA - Österreichische Finanzmarktaufsicht)
16:30, GM 3 Vortmann Hörsaal (Plus Energie Büro Hochhaus, 2. OG, Getreidemarkt 9)
Analytische Validierungsformeln für die Berechnung des besten Schätzwerts in der klassischen Lebensversicherung
Veranstaltungsreihe "Actuarial Modelling Club"

Martin Hahn (International Association of Insurance Supervisors)
16:30, GM 3 Vortmann Hörsaal (Plus Energie Büro Hochhaus, 2. OG, Getreidemarkt 9)
Insurance Capital Standard
Veranstaltungsreihe "Actuarial Modelling Club"

Reinhold Kainhofer (Generali Versicherung und AVÖ/ÖFdV)
17:00, GM 3 Vortmann Hörsaal (Plus Energie Büro Hochhaus, 2. OG, Getreidemarkt 9)
Überprüfung der Angemessenheit der Rententafel AVÖ 2005-R
Veranstaltungsreihe "Actuarial Modelling Club"

Gerd Müller und Mario Kasper (SCOR Rückversicherung Deutschland, SCOR Global Life)
17:00, Freihaus Hörsaal 6 (Freihaus, 2. OG, grün)
"Biological Age Model: Eine erweiterte Form der Risikobewertung in der Lebensversicherung"
Veranstaltungsreihe "Actuarial Modelling Club"

Frank Schiller (Munich Re)
17:00, Freihaus Hörsaal 6 (Freihaus, 2. OG, grün)
"Moderne Life-Style Produkte in der Lebensversicherung mit Big Data und Machine Learning"
Veranstaltungsreihe "Actuarial Modelling Club"

Julia Eisenberg (TU Wien, Univ. Liverpool)
09:30, seminar room DA gelb 05a (Freihaus, 5th floor, yellow area)
A new approach for satisfactory pensions with no guarantees
(Public Habilitation Talk) (close abstract)

The increase in longevity, the ultra-low interest rates and the guarantees associated to pension benefits have put significant strain on the pension industry. Consequently, insurers need to be in a financially sound position while offering satisfactory benefits to participants. In this talk, we consider a pension design that goes beyond the idea of annuity pools and unit-linked insurance products. The purpose is to replace traditional guarantees with low volatility, mainly achieved by collective smoothing algorithms and an adequate asset management. With the aim of offering security to the insured, we discuss the optimisation of some key variables of the proposed pension product to target both a high value of the initial pension and stable pension payments over time.
 

Jan-Philip Gamp, Ehsan Ayatollahi (Milliman, DE)
17:00, Freihaus Hörsaal 5 (Freihaus, 2. OG, grün)
"IFRS17 ?- unterschiedliche Bewertungsansätze in der Lebensversicherung"
Veranstaltungsreihe "Actuarial Modelling Club"

Gerold Petritsch (EVN)
17:00, Freihaus Hörsaal 5 (Freihaus, 2. OG, grün)
Über den aktuariellen Tellerrand hinaus: Data Science als Erfolgsfaktor in der Energiewirtschaft
Veranstaltungsreihe "Actuarial Modelling Club"

Christiane Elgert (FAM @ TU Wien)
14:00, conference room of the Deanery (Freihaus, 9th floor, green area - elevator only until 8th floor, then starecase)
Theory of Distribution-Constrained Optimization Problems
(Public PhD Thesis Defense) (close abstract)

Diese Arbeit beschäftigt sich mit verschiedenen Betrachtungsweisen von Optimierungsproblemen unter Verteilungsrestriktion. Zunächst kann das Problem als ein klassisches optimales Stoppproblem mit zusätzlichen Informationen aufgefasst werden. Hierbei ist die Verteilung der Stoppzeit gegeben. Es werden nanz- und versicherungsmathematische Produkte betrachtet, deren Auszahlungen auf stochastischen Prozessen beruhen. Der Zeitpunkt der Auszahlung ist zufällig und wird daher durch eine Stoppzeit modelliert, die Werte in einem vorgegebenen Zeitbereich annimmt. Diese Stoppzeit soll einer bestimmten Verteilung folgen und kann von dem zugrunde liegenden Auszahlungsprozess abhängen. Die vorgegebene Verteilung enthält zusätzliche Informationen, die bekannt sind oder auf die man Zugriff hat. Unser Ziel ist es, eine Abschätzung für den schlechtesten Fall, also der Worst-Case-Situation, abzuleiten. Zu diesem Zweck bestimmen wir das Supremum der zu erwarteten Auszahlung über alle Stoppzeiten, die die angegebene Randbedingung erfüllen. Ein anderer Ansatz des Problems besteht in der Verwendung von adaptierten zufälligen Wahrscheinlichkeitsma en anstelle von Stoppzeiten. Aus mathematischer Sicht handelt es sich bei dem betrachteten Problem um eine spezielle und erweiterte Version eines optimalen Stoppproblems. Desweiteren kann die Aufgabe auch als optimales Transportproblem formuliert und aus Sicht des Transports von Massen diskutiert werden. Ein wichtiger Aspekt bei der Betrachtung dieser Probleme ist die Frage nach einer optimalen Strategie, welche den Maximalwert annimmt. In dieser Arbeit wird die Existenz einer solchen optimalen Strategie für die verschiedenen Ansätze sowohl in diskreter als auch in kontinuierlicher Zeit bewiesen. Ferner werden obere und untere Schranken für die betrachteten Werte hergeleitet. Es werden zusätzlich auch Beispiele und Anwendungen zur Veranschaulichung dargestellt.
 

Sühan Altay (FAM @ TU Wien)
10:00, conference room of the Deanery (Freihaus, 9th floor, green area - elevator only until 8th floor, then starecase)
Interest Rate Modeling and Optimal Trading Portfolios with Dependence and Partial Information
(Public PhD Thesis Defense) (close abstract)

This dissertation deals thematically with two neighboring areas of financial mathematics. In Part I we consider a tractable defaultable term-structure model in a reduced-form setting that takes care of empirical stylized facts (negative instantaneous correlation between credit spread and risk-free rate) coherent with the mathematical and economical facts (non-negative intensity and risk-free rate) with an aim towards in better understanding of the dependence structure between credit and interest rate markets. In the remaining parts, we want to analyze optimal trading portfolios with specific dependence structures imposed on the stock prices with the view that not every model parameters are directly observable. In that respect, we analyze dynamic portfolio optimization problems under partial information related to a pairs trading in Part II and a market model with a large investor who can affect market sentiments in Part III.
 

Julia Eisenberg (TU Wien, AT & Univ. Liverpool, UK)
11:00-12:00, Sem.R. DA grün 05 (Freihaus, 5. OG, grüner Bereich
The time value of money in the actuarial framework (close abstract)

In this talk we consider some optimisation problems inspired by the topical questions in the non-life insurance branch.
Imagine an insurance company that needs to be rated by an internal service in order to make some principle decisions, for instance about additional reserves or time and amount of dividend payments. Therefore, the responsible actuaries have to quantify the risk connected to this company. As a possible risk measure one can use for instance the expected discounted dividend payments or even the old concept of ruin probabilities. The logic here could be the following: if the company is able to pay high dividends, then the company is doing well.
However, the performance of an arbitrary strategy cannot say much about the well-being of a company, but rather about the abilities of the company's management. Using the methods from the optimal control theory, we are looking for the strategies (and their properties) that maximize or minimize the chosen risks measures.
The findings will be illustrated by several examples.
 

Onnen Siems, Carina Götzen (Meyerthole Siems Kohlruss, DE)
16:30, GM 3 Vortmann Hörsaal (Plus Energie Büro Hochhaus, 2. OG, Getreidemarkt 9)
Aktuarielle Analyse von großen Telematikdatenmengen (Big Data)
Veranstaltungsreihe "Actuarial Modelling Club"

Praxis der Finanz- und Versicherungsmathematik 2018
Mittwoch, 26. September 2018, 9:30-17:15 Uhr
TU Wien, Freihaus Hörsaal 6, Anmeldung erforderlich: details

Praxis der Finanz- und Versicherungsmathematik 2018
Dienstag, 25. September 2018, 9:30-17:15 Uhr
TU Wien, Freihaus Hörsaal 6, Anmeldung erforderlich: details

Mikhail Arshinskiy (Deloitte Digital)
16:30, Hörsaal 13 Ernst Melan Hörsaal (Hauptgebäude der TU Wien, 2. OG,)
Digital cyber response: cost factors and probabilities
Veranstaltungsreihe "Actuarial Modelling Club"

Klaus Wegenkittl (ERGO Versicherung)
16:30, FH 8 Nöbauer HS (Freihaus, 2. OG, gelber Bereich)
PRIIP Basisinformationsblätter in der Lebensversicherung - Inhalt und Berechnungsmethoden
Veranstaltungsreihe "Actuarial Modelling Club"

Sabrina Mulinacci (University of Bologna, IT)
16:30, Seminarraum DB gelb 05A (Freihaus, 5th floor, yellow area)
C-convolution based stochastic processes in discrete time and financial prices dynamics
Colloquium in Statistics and Mathematical Methods in Economics

Sabrina Mulinacci (University of Bologna, IT)
16:30, Böcklsaal (TU Wien, Hauptgebäude, Stiege 1, 1. Stock)
Generalizations of the Marshall-Olkin distribution and applications
Vortragsreihe aus Finanz- und Versicherungsmathematik

Marc Linde (BELTIOS P&C GmbH, DE)
16:30, FH 8 Nöbauer HS (Freihaus, 2. OG, gelber Bereich)
Erfahrungen mit der versicherungsmathematischen Funktion in Schaden/Unfall
Veranstaltungsreihe "Actuarial Modelling Club"

Arpad Pinter (FAM @ TU Wien)
12:00, seminar room DA grün 05 (Freihaus, 5th floor, green area)
Small-Time Asymptotics, Moment Explosion and the Moderate Deviations Regime
(Public PhD Thesis Defense) (close abstract)

Die Dissertation "Small-Time Asymptotics, Moment Explosion and the Moderate Deviations Regime", verfasst von DI Arpad Pinter unter der Betreuung von Associate Prof. Dipl.-Ing. Dr.techn. Stefan Gerhold, ist in vier Teile gegliedert.
 
Im ersten Teil "Small-Maturity Asymptotics for the At-the-Money Implied Volatility Slope in Lévy Models" betrachten wir die at-the-money Steigung der impliziten Volatilität, d.h. die Ableitung der impliziten Volatilität nach dem Ausübungspreis, wenn die Restlaufzeit der dazugehörigen Option gegen 0 konvergiert. Das Hauptresultat quantifiziert das Verhalten der Steigung in exponentiellen Lévy-Modellen mit unendlicher Aktivität, die eine Brownsche Komponente aufweisen. Als technisches Nebenresultat, erhalten wir mit Hilfe der Mellin-Transformation eine asymptotische Entwicklung von at-the-money digitalen Callpreisen für kurze Restlaufzeiten.
 
Im zweiten Teil "Option Pricing in the Moderate Deviations Regime" betrachten wir Callpreise für kleine Restlaufzeiten in Diffusionsmodellen, in einem asymptotischen Regime ("moderately out-of-the-money"), dass zwischen den beiden gut untersuchten Fällen at-the-money und out-of-the-money interpoliert. Im Sinne der Moderate-Deviation-Theorie erhalten wir Abschätzungen erster und höherer Ordnung für Callpreise und implizite Volatilitäten.
 
Der dritte Teil "Moment Explosion in the Rough Heston Model" befasst sich mit einer Erweiterung des bekannten Heston-Modells, bei der die Pfade des Volatilitätsprozesses weniger glatt als beim klassischen Heston-Modell sind. Wir untersuchen die Explosionszeiten der momentenerzeugenden Funktion für alle möglichen Parameterwahlen. Im Falle einer endlichen Explosionszeit geben wir obere und untere Abschätzungen dafür. Unter Verwendung dieser Abschätzungen zeigen wir die Endlichkeit der kritischen Momente im Rough-Heston-Modell.
 
Der letzte Teil "Large-Strike Asymptotics in the 3/2-Model" widmet sich dem 3/2-Modell. Zunächst untersuchen wir die Dichtefunktion, die mittels Fourier-Transformation als ein Wegintegral in der komplexen Ebene dargestellt werden kann. Durch die Wahl eines transformierten Hankel-Weges und der expliziten Form der momentenerzeugenden Funktion ist es möglich, das asymptotische Verhalten der Dichtefunktion am positiven Ende zu bestimmen. Abschließend leiten wir daraus die asymptotische large-strike Entwicklung für die implizite Volatilität ab.
 

Zbigniew Palmowski (University of Wroclaw, Poland)
16:30, seminar room DA grün 06 (Freihaus, 6th floor, green area)
On optimal dividend problem for an insurance risk models with surplus-dependent premiums
(FAM Research Seminar) (close abstract)

In this talk we present an optimal dividend distribution problem for an insurance company which risk process with surplus-dependent premium (in the absence of dividend payments). Such a risk process is a particular case of so-called piecewise deterministic Markov process. The control mechanism chooses size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the moment of ruin and a penalty payment at the moment of ruin which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. We identify the associated HJB equation and find a necessary and su cient conditions for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function. We also analyze the dual risk process where the jumps of the risk process are nonnegative. A number of concrete examples are analyzed.
 

Piet Porkert (FAM @ TU Wien)
12:00, Zeichensaal 3 (Freihaus, 7th floor, green area)
Central and Non-Central Limit Theorems
(Public PhD Thesis Defense) (close abstract)

The dissertation is focused on the theory and applications of central limit theorems (CLTs) and non-central limit theorems (NCLTs). In Part I of the talk we deal with the limit behavior of random sums. We discuss a NCLT and rates of convergence. In this part, our primary emphasis is the new method of proof we propose. In Part II, we consider the limit behavior of semimartingales for small times. We give CLTs as well as functional CLTs on the process level with applications in mathematical finance. Part I and Part II are independent of each other.
 

Robert Schöftner (core dynamics GmbH, CH)
16:30, FH 8 Nöbauer HS (Freihaus, 2. OG, gelber Bereich)
Kreditrisikomodellierung für Versicherer - Praktische Kalibrierung von Portfoliomodellen und Rating-Tools
Veranstaltungsreihe "Actuarial Modelling Club"

Florian Gach, Martin Hahn (FMA - Österreichische Finanzmarktaufsicht)
16:30, GM 3 Vortmann Hörsaal (Getreidemarkt 9, Bauteil BA, 2.OG)
The Smith-Wilson curve - Mathematics and supervision
Veranstaltungsreihe "Actuarial Modelling Club"

Yuliya Mishura (Taras Shevchenko National University of Kyiv)
16:30, Seminarraum BD 02 (Getreidemarkt 4, building BD, 2nd floor)
Asymptotic methods and approximations on financial markets with stochastic volatility
Vortragsreihe aus Finanz- und Versicherungsmathematik

Praxis der Finanz- und Versicherungsmathematik 2016
(Berufsständisches Seminar)
TU Wien, Anmeldung erforderlich!

Praxis der Finanz- und Versicherungsmathematik 2016
(Mathematiker_innen in der Finanz- und Versicherungsbranche)
TU Wien, Anmeldung erforderlich!

Stefan Nörtemann (msg life central europe gmbh)
16:00, Freihaus Hörsaal 8 (Freihaus, 2. Stock, gelber Bereich)
"Big Data & Insurance Analytics im Spannungsfeld zwischen Innovation und Datenschutz"
Veranstaltungsreihe "Actuarial Modelling Club"

Onnen Siems, Carina Götzen (Meyerthole Siems Kohlruss, DE)
16:30, Freihaus Hörsaal 3 (Freihaus, 2. Stock, gelber Bereich)
Praxisbericht - "Data-Based Storm Modelling"
Veranstaltungsreihe "Actuarial Modelling Club"

Ronald Laszlo (Vienna Insurance Group), Karin Nowak (B&W Deloitte)
16:00, Freihaus Hörsaal 3 (Freihaus, 2. Stock, gelber Bereich)
"Herausforderung Immobilien unter Solvency II"
Veranstaltungsreihe "Actuarial Modelling Club"

Cetin Gülüm (FAM @ TU Wien)
10:00, Zeichensaal 3 (Freihaus, 7. floor, green area)
Consistency of Option Prices under Bid-Ask Spreads and Implied Volatility Slope Asymptotics
(Public PhD Thesis Defense) (close abstract)

We want to check European call option quotes for consistency under the assumption of a positive bid-ask spread on the underlying. Under the assumption that the bid-ask spread is bounded by a constant we will state sufficient and necessary conditions on the option prices, which ensure that they are consistent with an arbitrage free model. Also we will derive model independent arbitrage strategies for single and multiple maturities in case these conditions fail. If the bid-ask spread is not bounded by a constant we will show that it suffices to check each maturity separately for consistency.
 
The condition we will derive relies on a extension of a well known result (Strassen's theorem), which asserts that a stochastic process is increasing in convex order if and only if there is a martingale with the same marginal distributions. Such processes, or families of measures, are nowadays known as peacocks. We extend Strassen's theorem in a novel direction, relaxing the requirement on the martingale. Instead of equal marginal laws, we just require the laws to be within closed balls, defined by some metric on the space of probability measures. In our main result - which we will use to derive our consistency conditions - the metric is the infinity Wasserstein distance, but we also study other metrics.
 
Also, we will talk about small time asymptotics of the at-the money-implied volatility slope in exponential Lévy models and about portfolio optimisation using adaptive strategies.
 

Thorsten Rheinländer (FAM @ TU Wien)
19:00, Zeichensaal 3, Freihaus, 7.OG, grüner Bereich (gegenüber Lift)
Flash Crashes an den Börsen und automatisierter Hochfrequenzhandel
Öffentliche Veranstaltung des Lions Club Wien Ambassador (Ankündigung/Flyer)

Mario Kasper (SCOR Global Life SE, Vienna)
16:30, Freihaus Hörsaal 6 (Freihaus, 2. Stock, grüner Bereich)
Der graue Planet - Einige Gedanken zur Entwicklung der Lebenserwartung
Veranstaltungsreihe "Actuarial Modelling Club"

Stefan Thonhauser (TU Graz)
Über Optimierungsprobleme aus der Versicherungsmathematik
11:00, seminar room 105A (Freihaus, yellow area, 4th floor) (close abstract)

Das Ziel dieses Vortrages ist es, mein Forschungsgebiet vorzustellen. Im Kontext der Versicherungsmathematik entspringen stochastische Optimierungsprobleme aus Erweiterungen klassischer Risikomodelle um dynamische Interventionsmöglichkeiten. Nach einem kurzen Überblick möchte ich anhand konkreter Probleme illustrieren, welche mathematischen Methoden zu deren Lösung angewandt werden können.
 
Im zweiten Teil des Vortrages möchte ich zeigen wie man über eine "risikotheoretisch-praktische" Fragestellung zu einem Problem aus der Gleichverteilung kommt. Das praktische Problem ist in diesem Fall die Frage des Einflusses von schwer schätzbaren Abhängigkeitsstrukturen zwischen relevanten Risikofaktoren auf Risikomaße. Als Alternative, oder als robuster Ausweg, können natürlich extremale Schranken für das Risikomaß dienen. Diese Schranken lassen sich nun direkt mit einem Problem aus der Theorie der Gleichverteilung und des optimalen Transports verbinden.
 

Stefan Gerhold (FAM @ TU Wien)
Asymptotische Approximationen von Optionspreisen
9:30, seminar room 105A (Freihaus, yellow area, 4th floor) (close abstract)

Approximationen von Optionspreisen sind ein nützliches Werkzeug zur schnellen und robusten Kalibrierung von Finanzmarktmodellen. Exemplarisch werden einige Resultate und die verwendeten Methoden diskutiert (z.B. Sattelpunktmethode). Der Schwerpunkt wird auf einer aktuellen Arbeit über moderate deviations liegen (mit P. Friz und A. Pinter). Sie enthält Optionspreis-Asymptotiken in recht allgemeinen Diffusionsmodellen, wobei die Laufzeit gegen null konvergiert und der Strike gegen den Spot-Preis. Die erhaltene asymptotische Formel ist einfacher numerisch auszuwerten als vergleichbare Formeln im large-deviations-regime. Weiters erhält man einen Zusammenhang zwischen skew (Ableitung des volatility smiles) und Calloptions-Preisen.
 

Thomas Viehmann, Andrea Rauter (B&W Deloitte)
16:30, Hörsaal 6 (Hauptgebäude der TU Wien, Karlsplatz 13, Stiege 2, Erdgeschoß)
Negative Zinsen und hohe Volatilität - Herausforderungen für die Kapitalmarktmodellierung
Veranstaltungsreihe "Actuarial Modelling Club"

Alois Gisler (RiskLab, ETH Zürich)
16:30, GM 4 Knoller Hörsaal (Getreidemarkt 4, building BD, 2nd floor)
Das Chain-Ladder Reserve-Risiko neu betrachtet
Vortragsreihe aus Finanz- und Versicherungsmathematik

Tilmann Blümmel (FAM @ TU Wien)
12:30, seminar room 104 (Freihaus, green area, 5th floor)
Martingalzerlegungssätze und die Struktur von No Arbitrage
(Public PhD Thesis Defense) (close abstract)

Zunächst beweisen wir einen Martingalzerlegungssatz für beliebige lokale Martingale. Wir vergleichen diese Zerlegung, die wir Radon-Nikodym-Zerlegung nennen, mit der wohlbekannten Kunita-Watanabe-Zerlegung. Anhand verschiedener Beispiele illustrieren wir, dass die Kunita-Watanabe-Zerlegung im Allgemeinen nicht existiert. Nichtsdestotrotz, die Radon-Nikodym-Zerlegung existiert, und wir geben diese für die speziellen Beispiele an.
Desweiteren widmen wir uns der Struktur lokal quadratintegrierbarer Semimartingale. In mehreren "Strukturtheoremen" beleuchten wir die Verbindung zwischen der Struktur lokal quadratintegrierbarer Semimartingale einerseits und der Struktur strikt positiver Sigma-Martingaldichten andererseits. Während die Struktur lokal quadratintegrierbarer Semimartingale mit Hilfe von sogenannten Strukturbedingungen beschrieben werden kann, lässt sich die Struktur der Sigma-Martingaldichten mit Hilfe verschiedener Martingalzerlegungsätze beschreiben. Wir vergleichen unsere neuen Strukturbedingungen mit der wohlbekannten Strukturbedingung (SC) und der schwachen Strukturbedingung (SC'). Anhand zahlreicher Beispiele illustrieren wir, wie diese neuen Strukturbedingungen verwendet werden können, um strikt positive Sigma-Martingaldichten zu finden.
Schließlich wenden wir uns im letzten Teil der Modellierung mehrerer Phänomene zu, die im Zusammenhang mit der Anwesenheit großer Händler in Finanzmärkten stehen. Um diese Phänomene sauber trennen zu können, orientieren wir uns am Baukastenprinzip. Hierbei steht jeder einzelne Baustein für ein im Zusammenhang mit der Anwesenheit eines großen Händlers auftretendes Phänomen. Wir konzentrieren uns hier auf zwei Phänomene. Das erste betrifft die Art und Weise, wie ein großer Händler Einfluss auf den Preisprozess nehmen kann. Um ein Finanzmarktmodell mit großem Händler einführen zu können, das nicht im Widerspruch zu gängigen no-arbitrage-Annahmen für den kleinen Händler steht, widmen wir uns auch diesem Phänomen. Schließlich untersuchen wir das Nutzenmaximierungsproblem des großen Händlers. Dabei stellt sich heraus, dass ein großer Händler, trotz erfüllter no-arbitrage-Bedingungen, einen Finanzmarkt destabilisieren kann.
 

Pavel V. Shevchenko (CSIRO Australia)
16:30, Hörsaal 6 (Hauptgebäude der TU Wien, Karlsplatz 13, Stiege 2, Erdgeschoß)
Valuation of variable annuities with Guaranteed Minimum Withdrawal Benefit and capital protection options via stochastic control optimization
Vortragsreihe aus Finanz- und Versicherungsmathematik

Jonas Hirz (FAM @ TU Wien)
9:00, seminar room 104 (Freihaus, green area, 5th floor)
Advanced Conditional Risk Measurement and Risk Aggregation with Applications to Credit and Life Insurance
(Public PhD Thesis Defense) (close abstract)

First, we deal with a detailed analysis of several conditional risk measures. They provide the basis for an assessment of acceptable risk in a dynamic environment to cover unexpected losses. Based on the upper envelope and conditional lower quantiles, we define conditional distortion risk measures and give a collection of different properties. Conditional expected shortfall arises as a special case. Furthermore, we show a supermartingale property and the property of prospective increase in uncertainty. Weighted conditional expected shortfall also arises as a special case. We then introduce contributions to weighted conditional expected shortfall and prove several properties, including conditional coherence an Euler allocation. It is possible to derive contributions of subportfolios in order to identify main sources of risk. Secondly, using extended CreditRisk+, we develop a flexible framework to estimate stochastic life tables and to model aggregated risk in credit- and life insurance portfolios. Deaths are driven by common stochastic risk factors which may be interpreted as death causes like neoplasms, circulatory diseases or idiosyncratic components. Our approach provides an efficient, numerically stable algorithm for an exact calculation of the one-period loss distribution where various sources of risk are considered. Using publicly available data, we provide several estimation procedures. We conclude with a real world example using Australian data. In particular, our model allows stress testing and, therefore, offers insight into how certain health scenarios influence annuity payments of an insurer. Further applications of our model include modelling of stochastic life tables with corresponding forecasts.
 

René Knapp (UNIQA, Vienna)
16:30, Böcklsaal (Hauptgebäude der TU Wien, Karlsplatz 13, Stiege 1, 1. Stock)
Bestandsmanagement in der Lebensversicherung - ein Praxisbericht
Veranstaltungsreihe "Actuarial Modelling Club"

Jonas Hirz (FAM @ TU Wien)
16:30, for room see announcement
Ein Modell zur Risikoaggregation in Pensions- und Lebensversicherungsportfolios
Vortragsreihe aus Finanz- und Versicherungsmathematik

Stefan Thonhauser (TU Graz)
16:30, Seminarraum 107 (Freihaus, 6th floor, green section)
Optimal reinsurance in risk theory (close abstract)

In this talk I would like to give an overview on applications of optimal reinsurance in risk theory. I will start with a classical result of Raviv from insurance economics and subsequently move to the risk theoretical setting. After this overview I am switching to an actual problem of maximizing a performance measure for a classical surplus process by means of optimal reinsurance. In this situation one can characterize the value function of the problem and deduce a numerical procedure for its computation. Finally some examples illustrate the theoretical findings.
(Joint work with Arian Cani, University of Lausanne)
 

Lars Rösler (WU Wien)
17:30, Seminarraum 107 (Freihaus, 6th floor, green section)
Contagion Effects and Collateralized CVAs for Credit Default Swaps (part 2) (close abstract)

The talk is concerned with counterparty credit risk management for credit default swaps in the presence of default contagion. In particular, we study the impact of default contagion on credit value adjustments such as the BCCVA (Bilateral Collateralized Credit Value Adjustment) of Brigo et al. (2012) and on the performance of various collateralization strategies. We use the incomplete-information model of Frey and Schmidt (2012) as vehicle for our analysis. We find that taking contagion effects into account is important for the effectiveness of the strategy and we derive refined collateralization strategies to account for contagion effects.
 
The talk is based on a joint paper with Prof. Rüdiger Frey (WU Vienna).
 
Download the slides of the talk (part 1 and 2).
 

Lars Rösler (WU Wien)
Contagion Effects and Collateralized CVAs for Credit Default Swaps (part 1) (close abstract)

The talk is concerned with counterparty credit risk management for credit default swaps in the presence of default contagion. In particular, we study the impact of default contagion on credit value adjustments such as the BCCVA (Bilateral Collateralized Credit Value Adjustment) of Brigo et al. (2012) and on the performance of various collateralization strategies. We use the incomplete-information model of Frey and Schmidt (2012) as vehicle for our analysis. We find that taking contagion effects into account is important for the effectiveness of the strategy and we derive refined collateralization strategies to account for contagion effects.
 
The talk is based on a joint paper with Prof. Rüdiger Frey (WU Vienna).
 
Download the slides of the talk (part 1 and 2).
 

Cordelia Rudolph (FAM @ TU Wien)
Adapted Dependence with Applications to Financial and Actuarial Risk Management
(Public PhD Thesis Defense)
17:00, room "Zeichensaal 1 (Freihaus, green area, 8th floor)

Thorsten Schmidt (TU Chemnitz, DE)
Default Times not Avoiding Stopping Times: Defaultable Term Structure Modelling beyond the Intensity-Paradigm (close abstract)

Credit risk is typically either treated with a structural viewpoint pioneered in Merton (1974) or the reduced-form framework as in Jarrow & Turnbull (1995). The goal of this article is to provide a unified view on both approaches in a sufficiently generalized setup. The considered model allows for default times which have an intensity or occur at a fixed time with positive probability, henceforth not avoiding stopping times. A forteriori, the considered default times do not fall in the class of so-called intensity-based models.
 
The setup is intimately related to the theory of enlargement of filtrations, to which we provide a new class of examples where the Azema supermartingale contains jumps, both at predictable and totally inaccessible stopping times.
 
In the second part of the paper dynamic term structures prone to default risk in the framework of Heath-Jarrow-Morton (1992).
It turns out, that previously considered models in this framework lead to arbitrage possibilities. We propose a suitable, arbitrage-free generalization of this class with an additional stochastic integral containing atoms at predictable stopping time.
 

Yosef Rinott (The Hebrew University of Jerusalem, Israel)
15:00, seminar room 101C, Freihaus, 4th floor, green section
On methods for model selection (close abstract)

I will discuss some old and new ideas on model selection. As examples one can have in mind linear models with different subsets of covariates, Markov chains and autoregressive models of different orders, choosing among parametric models to estimate a distribution or density, etc.
The main goal is to choose a model that provides the best prediction for new data. Estimation of parameters can also be stated as a goal. Some methods aim towards finding the "true model", but more important are methods that select the best predictive model, when prediction is based on a given sample size. Overfitting due to choosing a model that is too detailed, and avoiding it, is a key issue.
Asymptotic properties of model selection methods will be discussed, but equally important are finite sample properties, which will be emphasized. Relevant buzzwords include AIC, BIC, C^p, Cross Validation.
 

Axel Helmert (COR & FJA, Vienna)
16:00, Freihaus Hörsaal 8 (Freihaus, 2nd floor, yellow section)
Low interest rate challenge: Trends in der Produktgestaltung
Veranstaltungsreihe "Actuarial Modelling Club"

Christiane Elgert (Universität Rostock, DE)
Numerische Lösung der Diffusionsgleichung bei variabler räumlicher Struktur (close abstract)

Die Diffusion von Stoffen in einer biologischen Zelle kann als dynamischer, räumlicher Prozess angesehen werden, welcher mittels der Diffusionsgleichung modelliert wird. Bei diesem Problem stellt die räumliche Struktur jedoch eine besondere Herausforderung dar. Alle Zellbestandteile, die sich von dem zu betrachtenden, diffundierenden Stoff unterscheiden, sind undurchdringliche Barrieren. Zur Simulation des Diffusionsproblems werden daher zwei Modellierungsansätze für die räumliche Struktur bei Nutzung verschiedener numerischer Verfahren, welche auf Finite-Differenzen-Diskretisierung beruhen, betrachtet.
 

Damir Filipovic (Swiss Finance Institute @ EPFL)
17:00, seminar room 11, University of Vienna, 1090 Vienna, Oskar-Morgenstern-Platz 1, 2nd floor
Linear-Rational Term Structure Models
(This talk is jointly organised with Uni Wien and WU Wien) (close abstract)

We introduce the class of linear-rational term structure models, where the state price density is modeled such that bond prices become linear-rational functions of the current state. This class is highly tractable with several distinct advantages: i) ensures non-negative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk premia, and iii) admits analytical solutions to swaptions. For comparison, affine term structure models can match either i) or ii), but not both simultaneously, and never iii). A parsimonious specification of the model with three term structure factors and one, or possibly two, unspanned factors has a very good fit to both interest rate swaps and swaptions since 1997. In particular, the model captures well the dynamics of the term structure and volatility during the recent period of near-zero interest rates.
 

Stefan Gerhold (FAM @ TU Wien)
15:15, Dissertantenraum, Freihaus, 8th floor, green section
Disproof of a conjecture by Rademacher on partial fractions
(Seminar Arbeitsgemeinschaft Diskrete Mathematik) (close abstract)

In his book Topics in Analytic Number Theory, Rademacher considered the generating function of partitions into at most N parts, and conjectured certain limits for the coefficients of its partial fraction decomposition. We carry out an asymptotic analysis that disproves this conjecture, thus confirming recent observations of Sills and Zeilberger (Journal of Difference Equations and Applications 19, 2013), who gave strong numerical evidence against the conjecture. (Joint work with Michael Drmota).
 

Petra Posedel (Zagreb School of Economics and Management, Croatia)
Asymptotic analysis for optimal estimating functions for a class of stochastic volatility models with jumps (close abstract)

In [1] Barndorff-Nielsen and Shephard introduced a class of stochastic volatility models in continuous time, where the instantaneous variance follows an Ornstein-Uhlenbeck type process driven by an increasing Lévy process. Those models have been studied from various points of view in mathematical finance and related fields. The martingale estimating function technique for parameter estimation in BNS-models was used in [2] to obtain estimators that are consistent and asymptotically normal. The obtained estimators are not efficient though. The aim of the present work is to develop estimators for BNS-models that are also optimal. Furthermore, the derivation of the asymptotic results for optimal estimators constructed using martingale estimating functions are analyzed in a more general setting. We study the consistency and asymptotic normality of the optimal estimator. Even though the estimator must be solved numerically, the asymptotic analysis of the resulting estimator can be performed. Moreover, the variance-covariance matrix of the estimator is calculated explicitly. The well-known theory from [3] for finding optimal estimating functions is reviewed and extended to a case of a bivariate Markov process. (Joint work with Friedrich Hubalek, TU Wien)
 
[1] Barndorff-Nielsen, O. E., Shephard, N. (2001) Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics, J. R. Stat. Soc. Ser. B Stat. Methodol. 63(2), 167-241.
 
[2] Hubalek, F., Posedel, P. (2012) Asymptotic analysis and explicit estimation of a class of stochastic volatility models with jumps using the martingale estimating function approach, Glasnik Matematicki. 48(1), 185-210.
 
[3] Heyde, C. C. (1997) Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation, Springer-Verlag, New York.
 

Julia Eisenberg (FAM @ TU Wien)
16:00, Besprechungsraum Galerie, TU Wien, Argentinierstraße 8, 1040 Wien (ground floor)
Optimal Consumption Under Deterministic Income
(This talk is organised by ECON @ TU Wien) (close abstract)

We consider an individual or household endowed with an initial wealth, having an income and consuming goods and services. The wealth development rate is assumed to be a deterministic continuous function of time. The objective is to maximize the discounted consumption over a finite time horizon. Via the Hamilton-Jacobi-Bellman approach, we prove the existence and the uniqueness of the solution to the considered problem in the viscosity sense. Furthermore, we derive an algorithm for explicit calculation of the value function and optimal strategy. It turns out that the value function is in general not continuous. The method is illustrated by two examples.
 

Christian Kuehn (TU Wien)
A Tour Through Stochastic Multiscale Dynamics via a Model Problem (close abstract)

In this talk, I shall outline some strategies to study stochastic multiscale problems for low-dimensional nonlinear SDEs. As a motivation, the influence of noise on oscillations will be considered. The results form a building block to understand complex oscillatory patterns arising in many applications. The main element of my talk will be the study of a local normal form of a folded node singularity in three dimensions via sample paths methods. Furthermore, I shall outline the prediction of tipping points and practical numerical methods for nonlinear SDEs.
 

Jonas Hirz (FAM @ TU Wien)
Talk within the seminar about High Frequency Trading:
Introduction to Cointegration with Applications to Finance (close abstract)

Literatur:
 
Johansen, S. Granger, C. & Mizon, G., ed. (1995), Likelihood-based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press.
 
Johansen, S., "Cointegration: Overview and Development", in: Handbook of Financial Time Series, pp 671-693.
 

Peter Friz (TU Berlin)
12:00, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
On the probability density function of baskets (close abstract)

The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In this note we discuss short time and small volatility expansions, respectively. The method works for general multi-factor models with correlations and leads to the analysis of a system of ordinary (Hamiltonian) differential equations. Surprisingly perhaps, even in two asset Black-Scholes situation (with its flat geometry), the expansion can degenerate at a critical (basket) strike level; a phenomena which seems to have gone unnoticed in the literature to date. Explicit computations relate this to a phase transition from a unique to more than one "most-likely" paths (along which the diffusion, if suitably conditioned, concentrates in the afore-mentioned regimes). This also provides a (quantifiable) understanding of how precisely a presently out-of-money basket option may still end up in-the-money.
 

Lukas Fabrykowski (TU Wien)
Talk within the seminar about High Frequency Trading

Daniel Thompson und Marcel Meier (B&W Deloitte)
16:00, Deloitte (Renngasse 1 / Freyung, 1010 Wien)
IFRS 4 Phase II - Aktuelle Entwicklungen und Herausforderungen
Veranstaltungsreihe "Actuarial Modelling Club"

PRisMa 2013
One-Day Workshop on Portfolio Risk Management
Hörsaal 6 (Karlsplatz 13, Main Building, ground floor)

Nikolai V. Kolev (University of Sao Paulo, Brazil)
16:30, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
Continuous Bivariate Distributions with Linear Sum of the Hazard Gradient Components and Actuarial Applications
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Eckhard Platen (University of Technology Sydney)
16:30, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
The Affine Nature of Aggregate Wealth Dynamics
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Henry Schellhorn (Claremont Graduate University, California)
15:00, Seminarraum 107 (Freihaus, 6th floor, green section)
A Representation Theorem For Smooth Brownian Martingales (close abstract)

We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented as an exponential of its value at a later time. The time-dependent generator of this exponential operator is equal to one half times the Malliavin derivative. This result can also be seen as a generalization of the semi-group theory of parabolic partial differential equations to the parabolic path-dependent partial differential equations introduced by Dupire (2009) and Cont and Fournié (2011). The exponential operator can be calculated explicitly in a series expansion, which resembles the Dyson series of quantum mechanics. Our continuous-time martingale representation result is proved by a passage to the limit of a special case of a backward Taylor expansion of an approximating discrete-time martingale. The latter expansion can also be used for numerical calculations. We will also show some applications to portfolio selection.
 

Eberhard Mayerhofer (Dublin City University, Ireland)
Mean Variance Optimisation with Transaction Costs (close abstract)

I report on ongoing joint work with Paolo Guasoni. We formulate appropriately a mean-variance optimality criterion in a Black-Scholes market with transaction costs and discuss, in particular, optimality of trading strategies derived by means of a fictious, frictionless market model.
 

Thomas Bruss (Université Libre de Bruxelles, Belgium)
Überleben und Lebensstandard, oder Grenzen der Gesellschaft - Schlussfolgerungen aus einem neuen Verzweigungsprozess-Modell
15:15, Freihaus Hörsaal 2 (Freihaus, 2nd floor, yellow section) (close abstract)

Zusammenfassung:
Was treibt die Menschheit dazu, viele verschiedene Gesellschaftsformen auszuprobieren? Gibt es Gesellschaftsformen, die für bestimmte Zielsetzungen und/oder Kriterien anderen Formen ganz klar überlegen sind? Wenn ja, welches sind diese Gesellschaftsformen, und inwieweit koennen diese als Richtlinien für andere dienen?
Der Vortrag kann auf diese Fragen im Rahmen eines speziellen Verzweigungsprozess-Modells Antworten geben. Dieses Modell ist einfach gehalten, erlaubt aber dennoch, wichtige Faktoren und Mechanismen einer jeden Gesellschaftsform mit zu berücksichtigen, nämlich Reproduktion, Schaffung von Ressourcen, individuelle Ansprüche und Interaktion von Individuen und Gesellschaft. Das Hauptresultat ist der "Hüllensatz" für Gesellschaftsformen. Dieser zeigt unter anderem, dass gewisse Gesellschaftsformen, mit denen die Menschheit schon Erfahrungen sammeln konnte, der Grenze des "Möglichen" schon sehr nahe gekommen sind.
Schlüsselworte:
Konvergenz (i.p., a.s., komplette), modifizierte Borel-Cantelli Lemmata, Aussterbekriterien, empirische VF, Stoppzeiten fuer Ordnungsstatistiken,Überlebenschancen und Lebensstandard, kritische Kurven, Laissez-faire Gesellschaft, Merkantilismus, aufgeklärte Formen, Marxismus, (Ultra)-Kommunimus, (Ultra)-Kapitalismus
Zielgruppe:
Mathematiker (Stochastik), Ökonometriker, Makro-Ökonomen, Anthropologen, Sozialwissenschaftler.
 

Karin Hirhager (FAM @ TU Wien)
Adapted Dependence with Applications to Financial and Actuarial Risk Management
(Public PhD Thesis Defense)
16:00, Conference room of the Deanery (Freihaus, green area, 9th floor) (close abstract)

This thesis is about financial and insurance products with pay-outs that are determined by the value of a stochastic process at a random point in time. This time point is modeled by a stopping time that follows a given distribution and may depend on the stochastic process modeling the pay-out. The supremum over the expected pay-out is considered. An extension of the problem is given by the use of adapted random probability measures, which model a withdrawal measured in percentage.
An important aspect in considering this problem is the question of an optimal strategy. In a discrete-time setting the existence of an optimal strategy, which is not unique in general, is proven.
The presented problem has two simple bounds. A lower bound is found by assuming independence and an upper bound is given by the value of an optimal stopping problem with the same underlying process. A number of other bounds are derived. Some of them are valid for the problem in general, while others depend on the structure of the underlying process.
It is possible to find both an optimal strategy and the resulting value for certain classes of stochastic processes. These include independent processes, processes with uncorrelated increments and processes for which the predictable process in the Doob decomposition has uncorrelated increments.
In continuous time we consider stopping times and stochastic transition kernels. A discrete approximation is presented that can help transfer the results found in discrete time to some in continuous time.
Various applications in the areas of financial and actuarial mathematics are discussed. These include unit-linked life insurances, a stochastic model for health insurances, the liquidation of an investment portfolio or the valuation of swing options.
 

Jan Widenmann (LMU Mathematics Institute, Munich)
Pricing and hedging insurance claims in hybrid markets (close abstract)

The merging of different types of markets is a challenging issue in nowadays financial and actuarial mathematics. Various influences and dependencies need to be incorporated in the models. The presented work addresses this issue by introducing intensity-based pricing and hedging schemes for a large class of insurance products. The basic idea in this context is to model the insured person’s progress of sojourning the different states of an insurance policy as an F-doubly stochastic Markov chain. The advantage of this class of processes is that they are generated by stochastic intensity processes, which can be modeled very generally. In this context, pricing schemes for unemployment insurance contracts are presented. The generating intensity processes here are driven by several micro- and macro-economic risk factors, making the resulting insurance premium very flexible.
Regarding the hedging purpose for insurance products, quadratic hedging approaches are applied to general insurance contracts. The results are further specified within an affine setting for the intensity processes. A simulation study for the remaining risk of mean-variance hedging for several life-insurance products with respect to longevity bonds is presented.
 

Florian Leisch (TU Wien, OeNB)
Stochastic Portfolio Theory from the Point of View of Risk Management
(Public PhD Thesis Defense)
17:00, Seminar room 104 (Freihaus, 5th floor, green section) (close abstract)

Deutschsprachige Kurzfassung:
Die vorliegende Arbeit befasst sich mit dem Themengebiet der stochastischen Portfolio Theorie und Problemen und Fragestellungen, die in diesem Feld auftreten. Diese Theorie verfolgt einen deskriptiven Ansatz für das Langzeitverhalten von Preisen, der im Gegensatz zu klassischen Ansätzen in der Portfolioselektion steht, wo die explizite Kenntnis von Drifts und Nutzenfunktionen erforderlich ist. Eingangs wird ein Überblick über fundamentale Konzepte und Forschungsergebnisse in der Stochastischen Portfolio Theorie gegeben, die wesentlich durch die wegweisenden Arbeiten von Fernholz und Karatzas geprägt wurden.
Wir untersuchen in weiterer Folge das bemerkenswert stabile Verhalten zweier ökonometrischer Eigenschaften, nämlich die Kapitalverteilungsstruktur und die Dynamik der Entropie des Marktes sowie deren Reproduktion durch das verwendete Marktmodell. Mit dem Ziel, diese beiden Eigenschaften korrekt abzubilden, entwickeln wir ein Marktmodell ausgehend von einer bestimmten Klasse positiver affiner Prozesse. Unsere Intention ist es, sowohl das Verhalten der genannten Eigenschaften zu reproduzieren, als auch die beobachtbaren Korrelationsstrukturen in Aktienmärkten zu berücksichtigen - ein essentieller Aspekt aus Sicht des Risikomanagements. Im ersten Schritt werden unabhängige quadrierte Brownsche Bewegungen als Ausgangspunkt für ein Aktienmarkt-Modell verwendet, wobei wir zeigen, dass dieser Ansatz die beobachtbare Struktur der Kapitalverteilung sehr gut reproduziert. Im zweiten Schritt erweitern wir unser Modell um eine instantane Kovarianzstruktur auf Basis von GARCH(1,1) Volatilitätsschätzern und der Korrelationsstruktur der Marktdaten. Diese Vorgehensweise liefert eine im Zeitverlauf veränderliche Kovarianzstruktur und vermeidet explizite Elliptizitätsannahmen. Durch die Anwendung von Modellierungsansätzen aus der affinen Kategorie und durch eine adäquate Modellierung der Abhängigkeitsstrukturen zwischen einzelnen Aktien zeigen wir empirisch, dass es gelingt, die Struktur der Kapitalverteilung und die Dynamik der Marktentropie zusammen mit der allgemeinen Dynamik des Aktienmarktes gut zu reproduzieren.
Der entwickelte Modellansatz erweist sich überdies als geeignet für Anwendungen im Bereich des Risikomanagements. Der Vergleich des korrelierten Modells mit einem Modell auf Basis unabhängiger Aktien verdeutlicht, dass die Einbindung einer adäquaten Korrelationsstruktur zu einer deutlichen Verbesserung der Struktur des langfristigen Marktverhaltens führt und dass wir hierdurch ein realistisches Maß an Marktvolatilität erhalten. Diese Aspekte unterstreichen die Eignung des vorgeschlagenen korrelierten Marktmodells für Anwendungen im Risikomanagement, wie beispielsweise die Berechnung von Risikomaßen und längerfristigen Benchmark-Simulationen.
 

Nicoletta Gabrielli (ETH Zurich)
Pathspace representation of Affine processes (close abstract)

When facing the problem of pricing path dependent options, an efficient method for the simulation of the trajectories of the underlying stock is essential. However, in some cases, e.g. when the vector field lacks the Lipschitz regularity, standard discrete approximation schemes cannot be applied.
We therefore seek high order and geometry preserving discretization methods.
The starting point of our analysis is the investigation of the evolution of an Affine process not only in terms of time, but also with respect to its initial value.
Inspired by the well known relationship between Feller diffusion and compound Poisson processes, we develop a representation of Affine processes as realizations of path-valued Lévy processes which leads to a new perspective on numerics of their paths.
 

Christian Genest (McGill University, Montréal, Canada)
17:30
Accounting for extreme-value dependence in multivariate data.
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Johanna Nešlehová (McGill University, Montréal, Canada)
16:30
Wie kann man Abhängigkeiten zwischen diskreten und gemischten Risiken aufdecken?
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Stefan Gerhold (FAM @ TU Wien)
15:15, Dissertantenraum, Freihaus, 8. Stock, grüner Bereich
Some traces of discrete mathematics in mathematical finance,
Seminar Arbeitsgemeinschaft Diskrete Mathematik, details (close abstract)

While mathematical finance usually draws upon areas such as stochastic analysis and PDE theory, sometimes there is occasion to use methods known from discrete mathematics. In this talk we will sketch three such instances: Lagrange inversion in transaction cost modelling, the saddle point method in a local volatility approximation, and orthogonal polynomials in American option pricing.
Based on joint works with P. Friz, P. Guasoni, J. Muhle-Karbe, and Walter Schachermayer.
 

Andreas Kyprianou (University of Bath)
Multi-level Wiener-Hopf Monte-Carlo simulation for Lévy processes (close abstract)

We introduce a completely new Monte-Carlo method for simulating the paths of Lévy processes and their maximum over finite time horizon. Moreover we show how this method naturally extends to the method of multi-level Monte-Carlo simulation. The way in which these algorithms are constructed turns out to offer straightforward proofs for the rate of convergence which, to leading order, are the fastest rate that one can hope for. Applications in mathematical finance and insurance mathematics will also be made clear in the talk.
 

Piet Porkert (FAM @ TU Wien)
Small time central limit theorems for semimartingales with applications (close abstract)

We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with locally bounded and continuous coefficients. The limit theorems are subsequently extended to functional central limit theorems on the process level. We present two applications of the results in the field of mathematical finance: to the pricing of at-the-money digital options with short maturities and short time implied volatility skews.
This is joint work with S. Gerhold, M. Kleinert and M. Shkolnikov.
 

Carole Bernard (University of Waterloo)
16:30, seminar room 107 (Freihaus, 7th floor, green section)
Mean-Variance Optimal Portfolios in the Presence of a Benchmark with Applications to Fraud Detection
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Irene Schreiber (LMU Munich)
16:30, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
Risk-Minimization for Life Insurance Liabilities
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

PRisMa 2012
One-Day Workshop on Portfolio Risk Management
Hörsaal 6 (Karlsplatz 13, Main Building, ground floor)

Peter Eichelsbacher (Ruhr-Universität Bochum)
Die Steinsche Methode und Anwendungen - Teil 2 (close abstract)

Die Steinsche Methode wird seit ihrer Einführung in 1972 zur Herleitung von Grenzwertsätzen sowie zur Bestimmung von Konvergenzraten bei diesen Sätzen verwendet. Dabei gibt es in jüngster Zeit viele Beiträge, die die Methode selbst weiterentwickelt haben. In den beiden Vorträgen (8. Mai und 12. Juni 2012) wollen wir einen Einblick in die Methode geben. Darüberhinaus werden Anwendungen aus dem Bereich von Modellen der statistischen Mechanik vorgestellt. Teile des Vortrags entstammen einer Zusammenarbeit des Vortragenden mit seinem Kollegen Matthias Löwe (Universität Münster) sowie mit seinem Mitarbeiter Bastian Martschink (Ruhr-Universität Bochum).
 

Stefano De Marco (TU Berlin)
Large deviations for diffusions and local volatilities (close abstract)

Motivated by Gyongy's (86) projection result for Ito SDEs and by its applications in the context of volatility modeling in finance, we consider large deviation problems for densities of diffusions in a small-noise regime, focusing on marginals (i.e. the densities of components of the process) and on the law of the diffusion conditioned to be in an affine subspace at final time. For stochastic volatility models enjoying certain scaling properties (i.e. the Stein-Stein model), this eventually leads to the large-strike asymptotic behavior of the 'equivalent' local volatility.
 

Peter Eichelsbacher (Ruhr-Universität Bochum)
Die Steinsche Methode und Anwendungen - Teil 1 (close abstract)

Die Steinsche Methode wird seit ihrer Einführung in 1972 zur Herleitung von Grenzwertsätzen sowie zur Bestimmung von Konvergenzraten bei diesen Sätzen verwendet. Dabei gibt es in jüngster Zeit viele Beiträge, die die Methode selbst weiterentwickelt haben. In den beiden Vorträgen (8. Mai und 12. Juni 2012) wollen wir einen Einblick in die Methode geben. Darüberhinaus werden Anwendungen aus dem Bereich von Modellen der statistischen Mechanik vorgestellt. Teile des Vortrags entstammen einer Zusammenarbeit des Vortragenden mit seinem Kollegen Matthias Löwe (Universität Münster) sowie mit seinem Mitarbeiter Bastian Martschink (Ruhr-Universität Bochum).
 

Miklos Rasonyi (University of Edinburgh)
13:00, Seminarraum 101A ("Freihaus", green section, 3rd floor)
Optimal investment: from risk-averse to behavioural agents (close abstract)

Classical investment problems assume that economic agents are risk-averse. This corresponds to using concave utility functions to describe agents' preferences. More recently, non-concave utilities were proposed and distortions of the probability measure were also considered.
 
We are dealing with optimal investment for an agent whose behaviour is characterized by a possibly non-concave utility function and by probability distortions. This new setting poses several mathematical challenges and exhibits a number of unexpected phenomena.
 
In discrete-time multiperiod models we discuss the well-posedness of this investment problem and show the existence of optimal strategies under suitable conditions. We also have a look at what happens in continuous-time, in particular, we provide a sufficient and (essentially) necessary condition for the Black-Scholes model in the case of power-like utilities and distortion functions.
 

Stefan Weber (Leibniz Universität Hannover)
9:00, Seminarraum 101B ("Freihaus", green section, 3rd floor)
Liquidity-Adjusted Risk Measures (close abstract)

Liquidity risk is an important type of risk, especially during times of crises. As observed by Acerbi & Scandolo (2008), it requires adjustments to classical portfolio valuation and risk measurement. Main drivers are two dimensions of liquidity risk, namely price impact of trades and limited access to financing. The talk discusses a cash-invariant liquidity-adjusted risk measure that can naturally be interpreted as a capital requirement. The difference between our construction and the one of Acerbi & Scandolo (2008) is analyzed in the framework of capital requirements using the notion of eligible assets, as introduced by Artzner, Delbaen & Koch-Medina (2009). Numerical case studies illustrate how price impact and limited access to financing influence the liquidity-adjusted risk measurements.
 

Thorsten Schmidt (Chemnitz University of Technology)
16:00, Seminar Room 107
Kreditrisiken und deren Modellierung (close abstract)

In den letzten 20 Jahren hat sie die Modellierung von Kreditrisiken als ein wichtiges Gebiet in der Finanzmathematik etabliert. Die Kreditkrise in 2008 und der Jahren danach sowie die aktuellen Diskussionen innerhalb der EU-Länder unterstreichen die Wichtigkeit eines tieferen Verständnisses von Kreditrisiken. In diesem Vortrag wird zum einen ein allgemeiner Rahmen für die Modellierung von Kreditrisiken vorgestellt, in welchem verschieden Aspekte beantwortet werden können. In diesem Vortrage sollen die arbitragefreie Modellierung, Bewertung und Absicherung von Risiken sowie Ratings behandelt werden.
 

Thorsten Rheinländer (London School of Economics)
14:00, Seminar Room 107
Self-dual stochastic processes and semi-static hedging for realistic price processes (close abstract)

Semi-static hedging of path-dependent barrier options by non-vanilla European ones has caught quite some attention among both academics and practitioners. In fact, the common practice is questionable since it would only work out in case the stochastic log-returns are conditionally symmetric which is unrealistic. We show in the context of continuous stochastic volatility models how to obtain the hedging strategy via a change to an asymmetric risk measure under which all characteristics can be obtained easily. These considerations lead to a general as well as a dual general form of self-duality. In practice, the hedging strategy would involve instruments written on the cumulative variance.
In the Lévy world, the notion of quasi self-duality is linked to an exponentially decaying factor when comparing the right- and left tails of the Lévy measure density. Lifting symmetric processes to their stochastic exponentials, a certain Möbius transform is involved. Since for non-vanishing order parameter of quasi self-duality two martingale properties have to be satisfied simultaneously, there is a non-trivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We discuss several important properties of this equation and, for some well-known models, we derive a family of closed-form inversion formulae leading to parametrisations of sets of possible combinations in the corresponding parameter spaces of Lévy driven models. As for continuous stochastic volatility models, we provide a structure result for quasi self-dual processes. Moreover, we give a characterisation of continuous Ocone martingales via a strong version of self-duality of their stochastic exponentials. Finally, we discuss an example of a non-Ocone martingale which is process, but not conditionally symmetric, and whose stochastic exponential is a strict local martingale.
The talk is based on joint works with Michael Schmutz, University of Bern, and on ongoing work with Zhanyu Chen, London School of Economics.
 

Vicky Fasen (ETH Zürich)
CANCELLED!!!

Stefan Gerhold (FAM @ TU Wien)
8:30, Seminar Room 107
Portfolio Optimization under Transaction Costs (close abstract)

Introducing transaction costs into models of financial markets makes trading strategies more realistic, e.g., concerning the amount of trading volume. We discuss how different objectives and agent preferences affect the optimal strategy and its growth rate, and other quantities of economic interest. All these are obtained in semi-explicit form, and admit simple and accurate asymptotic expansions for small transaction costs. The main technical tool is a fictitious frictionless shadow market, which is equivalent to the transaction cost market. We conclude with a view on some of the open problems in the field. (Based on joint work with Paolo Guasoni, Johannes Muhle-Karbe, and Walter Schachermayer)
 

Mykhaylo Shkolnikov (MSRI, Berkeley, USA)
15:00, Seminar Room 107
On diffusions interacting through their ranks (close abstract)

We will discuss systems of diffusion processes on the real line, in which the dynamics of every single process is determined by its rank in the entire particle system. Such systems arise in mathematical finance and statistical physics, and are related to heavy-traffic approximations of queueing networks. Motivated by the applications, we address questions about invariant distributions, convergence to equilibrium and concentration of measure for certain statistics, as well as hydrodynamic limits and large deviations for these particle systems. Parts of the talk are joint work with Amir Dembo, Tomoyuki Ichiba, Soumik Pal and Ofer Zeitouni.
 

Ramin Okhrati (FAM @ TU Wien)
Defaultable claims under finite variation Lévy processes (close abstract)

In the context of locally risk-minimizing approach, we discuss the problem of pricing and hedging of defaultable claims and their Föllmer-Schweizer decompositions. It is supposed that the market is made of only two assets, the risky asset that is modeled by a finite variation Lévy process and a risk-free one. Normally, risk management techniques of defaultable claims are carried out when the underlying process is continuous, the derivative is path independent, or the probability measure is risk-neutral. Especially continuity has been a crucial assumption in most of financial models. In this talk, we show how martingale techniques can be used in a certain framework to challenge all the above assumptions, specifically the continuity assumption. Finally we investigate the existence of a risk-free defaultable claim in the market.
 

Hansjörg Albrecher (University of Lausanne)
15:30, Freihaus Hörsaal 4 (Freihaus, 2nd floor, yellow section)
Messung von Versicherungsrisiken und das Omega-Modell
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

PRisMa 2011
One-Day Workshop on Portfolio Risk Management
Hörsaal 6 (Karlsplatz 13, Main Building, ground floor)

Zehra Eksi (Vienna Institute of Finance)
Pricing and Hedging of Single Tranche CDOs (close abstract)

In this study we fist review the framework introduced in [1] and examine the uniqueness of the equivalent local martingale measure (ELMM) in the defaultable (T,x)-bond market. We show that the ELMM is unique. Following this, we specify an affine two factor (stochastic drift) model for the pricing and hedging of single tranche synthetic CDOs. We estimate the affine factor model on the iTraxx Europe data. As the main tool for the estimation of the affine factor model we use quasi maximum likelihood based on a Kalman filter. Estimation results show that the two factor stochastic drift model is successful in terms of fitting the market data even for super-senior tranches. Apart from estimating the model, we analyze the real world performance of two hedging strategies, namely the variance minimizing and regression based hedging. We also run a simulation analysis where normal and extreme loss scenarios are generated via method of importance sampling. Finally we assess the hedging strategies under these more general scenarios.
 
[1] D. Filipovic, L. Overbeck, and T. Schmidt. ''Dynamic CDO term structure modeling''. Mathematical Finance, 2009. ISSN 1467-9965.
 

Carole Bernard (University of Waterloo)
16:30, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
Optimal investment under state-dependent constraints.
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Gregory Temnov (University College Cork, Ireland)
Characterization of memory states of the Preisach operator with stochastic inputs (close abstract)

We consider the long term effect of stochastic inputs on the state of an open loop system which exhibits the so-called return point memory. An example of such a system is the Preisach model; more generally, systems with the loop-type input-state relationship. We focus on the characterisation of the expected memory configuration after the system has been effected by the stochastic input for sufficiently long period of time. In the cases where the input is given by a random walk and by the Wiener process, simple closed form expressions for the probability density of the vector of the main input extrema recorded by the memory state, and scaling laws for the dimension of this vector, are derived. If the input is given by a general diffusion process, we show that the distribution of the memory elements can be obtained from a Markov chain scheme which is derived from the solution of an associated one-dimensional escape type problem. Explicit formulas for the joint probability densities of the main extrema are obtained for the Ornstein-Uhlenbeck input process. Finally, we discuss a possible interpretation of the studied model in financial applications.
Joint work with Dmitry Rachinskii and Andreas Amann (University College Cork).
 

Flavia Giammarino (London School of Economics)
Indifference Pricing with Uncertainty Averse Preferences
10:30 (close abstract)

We consider the indifference valuation of an uncertain monetary payoff from the perspective of an uncertainty averse decision-maker. We study how the indifference valuation depends on the decision maker's attitudes toward uncertainty. We obtain a characterization of comparative uncertainty aversion and various characterizations of increasing, decreasing, and constant uncertainty aversion.
 

Stefan Gerhold (FAM @ TU Wien)
Special Functions: From Lindelöf Integrals to Volatility Smiles
(Habilitationskolloquium)
16:15, FH Hörsaal 4

Stefan Gerhold (FAM @ TU Wien)
Transaction Costs made Tractable (close abstract)

In a market with one safe and one risky asset, an investor with a long horizon and constant relative risk aversion trades with constant investment opportunities and proportional transaction costs. We derive the optimal investment policy, its welfare, and the resulting trading volume, explicitly as functions of the market and preference parameters, and of the implied liquidity premium, which is identified as the solution of a scalar equation. For small transaction costs, all these quantities admit asymptotic expansions of arbitrary order. The results exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also derived explicitly. (Joint work with Paolo Guasoni, Johannes Muhle-Karbe, and Walter Schachermayer)
 

Eberhard Mayerhofer (Vienna Institute of Finance)
Part A: Affine processes on the positive semidefinite d x d matrices don't jump too wildly.
Part B: Wishart processes and Wishart distributions: Relations and Realizations. (close abstract)

Part A:
I explain why for dimension d>1 these processes exhibit jumps of finite variation only. The result is quite new and it allows a simplification of the theory by Cuchiero, Filipovic, Mayerhofer and Teichmann (AAP 2011).
 
Part B:
Wishart distributions are a natural generalization of non-central chi-squared distributions as well as natural gamma distributions on the positive real line (dimension d=1). The generalization concerns the dimensionality: For d>1 the probably most useful generalization yields the class of non-central Wishart distributions on the cone of positive semi-definite matrices. I apply the recent theory of affine processes on positive semidefinite matrices to derive nontrivial restrictions on the shape and non-centrality parameter, the so-called 'rank condition'.
 

Jonas Hirz (University of Salzburg)
Optimizing Investment Strategies under a General Approach to Cost-Efficiency (close abstract)

Bernard and Boyle (2010) employed the preference free framework introduced by Dybvig (1988) and Cox and Leland (1982, 2000) to optimize the structure of dynamic investment strategies. They give a characterization of the strategy with the lowest cost among the set of all strategies with the same payoff distribution. This thesis generalizes their results by relaxing the assumption on the continuity of the state-price density at maturity. First we provide the theoretical background by solving a general stochastic optimization problem, whereas we give modest generalizations to previous results on this topic and implement the concept of ω-monotonicity. Moreover, we adapt a method, taken from the textbook of Shorack und Wellner (1986), to solve the stated problem by introducing an enlarged product space. In the next step we adopt these results to find cost-efficient investment strategies, whereas our general approach covers discrete cases as in Dybvig (1988), as well as continuous cases as in Bernard and Boyle (2010). Furthermore we point out the influence of cost-efficiency on the behaviour of profit-seeking investors in a fairly general preference framework and its connection to first-order stochastic dominance. Subsequently we analyse the optimization of investment strategies under the preference framework of risk-averse investors and its relationship to second-order stochastic dominance. To show the need of our extensions, we take a closer look at put and call options in a special onedimensional Black-Scholes market, where we finally point out fundamental differences to the case of constant coefficients.
 

Umut Cetin (London School of Economics)
16:30, FH Hörsaal 3
Explicit construction of a dynamic Bessel bridge of dimension 3 (close abstract)

Given a deterministically time-changed Brownian motion Z starting from 1, whose time-change V (t) satisfies V (t) > t for all t > 0, we perform an explicit construction of a process X which is Brownian motion in its own filtration and that hits zero for the first time at V (S), where S := inf {t > 0 : Z_t = 0}. We also provide the semimartingale decomposition of X under the filtration jointly generated by X and Z. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process X may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time V (S). We call this a dynamic Bessel bridge since S is not known at time 0 but is slowly revealed in time by observing Z. Our study is motivated by insider trading models with default risk. (this is a joint work with Luciano Campi and Albina Danilova)
 

Esther Frostig (University of Haifa, Israel)
A Markov Additive Risk process with dividend barrier and phase type claims (close abstract)

In the risk theory literature the expected discounted dividends and the Gerber-Shiu function are usually studied by solving stochastic differential equations. In this talk we study a risk process in random environment where at each state the process behaves as a compound Poisson process perturbed by Brownian motion, besides, a transition of the modulating state has a positive probability of triggering a claim arrival. We study the expected discounted dividends, the distribution of the dividends, the Gerber-Shiu function by applying tools from the theory of spectrally negative Lévy processes. When the claims are phase-type distributed we obtain algorithms that calculate these quantities.
 

Piet Porkert (TU Wien)
On Weak Solutions to Stochastic Differential Equations in Finite and Infinite Dimensions (close abstract)

The notion of weak solution allows establishing solutions of stochastic ordinary differential equations when strong solutions might not exist. We discuss the existence of weak solutions in finite and infinite dimensions.
 

Michael Punz (Munich Re, Germany)
9.30-11.00, Seminar room 101C
Volatilitätsderivate (close abstract)

In diesem Vortrag stellen wir Strategien zur Replikation und Preisfindung von den wichtigsten Volatilitätsderivaten vor. Der Preis des Variance Swaps kann aus Optionspreisen abgeleitet werden, dies ist unter sehr allgemeinen Bedingungen an den Aktienpreisprozess möglich. Für die Preisbestimmung des Volatility Swaps nehmen wir zunächst an, dass der Aktienpreisprozess und der Volatilitätsprozess unabhängig sind, um ähnliche Resultate zu erhalten. Wir gehen dann genauer auf die Arbeit "Robust Replication of Volatility Derivatives" von P. Carr und R. Lee ein, in welcher diese unrealistische Annahme abgeschwächt wird.
 

Tilmann Blümmel (Albert-Ludwigs-University, Freiburg, Germany)
Anmerkungen zur Nutzenmaximierung (close abstract)

Der Vortrag begingt mit einen kurzen, chronologischen Überblick zum Thema "Nutzenmaximierung", der in der Vorstellung der Arbeit "Utility Maximization in Incomplete Markets for Unnbounded Processes” von S. Biagini und M. Frittelli mündet. Diese Arbeit stellt erstmals ein theoretisches Konzept vor, das es erlaubt, das klassische, ökonomische Problem der Maximierung des erwarteten Nutzens auch im Fall eines nicht notwendigerweise lokal beschränkten Preisprozesses zu behandeln. Wir gehen dabei genauer auf die in dieser Arbeit neu eingeführte Klasse der W-zulässigen Handelsstrategien ein, die von einer Verlustvariablen abhängt. Mit Hilfe der Theorie der Orlicz-Räume und der sogenannten Sigma-Lokalisation lassen sich diese neuen Ideen auch als Kriterien an den zugrundeliegenden Preisprozess formulieren. Abschließend beschäftigen wir uns in diesem Zusammenhang genauer mit der Klasse der Levy-Prozesse und speziell mit dem Levy-Maß des Preisprozesses. Dieses ermöglicht u.a. eine anschauliche Interpretation der oben erwähnten neuen Konzepte von S. Biagini und M. Frittelli.
 

Nadezhda Sholokhova (Ufa State Aviation Technical University, Russia)
Commercial bank deposit portfolio optimization (close abstract)

We consider the problem of banking deposit portfolio management within the limits of asset-liability management. Under this consideration we try to identify several sub tasks, such as, interest rates price-setting, forecasting the volume of accumulated funds within the fixed period of time etc. Also we try to specify several factors and their influence on the deposit product life cycle.
 

Carlo Sgarra (Politecnico di Milano, Italy)
Stochastic Ordering with GARCH Models (close abstract)

Stochastic ordering properties of financial models provide several useful informations on option prices, in particular on bounds. In spite of the huge numbers of results of this kind obtained in the continuous time setting, not so many results on discrete time models are available. The talk will present some preliminary results on stochastic orders in a GARCH model framework. We shall discuss both the issue related to stochastic ordering of risk-neutral measures and stochastic ordering of models.
 

Nicole Bäuerle (Karlsruher Institut für Technologie)
16:45, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
The Relaxed Investor with Partial Information
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Jürgen Hartinger (Kärntner Landesversicherung)
8:30-16:00, Theresianumgasse Hörsaal 1 (1040 Wien, Theresianumgasse 27)
Aktu(ari)elle Steuerungs- und Solvabilitäts-Konzepte in der Lebensversicherung
registration mandatory, please find details here

Paolo Guasoni (Dublin City University, Ireland)
13:15, FH Hörsaal 4
Abstract, Classic, and Explicit Turnpikes (close abstract)

Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. The abstract turnpike, valid in a general semimartingale setting, states that final payoffs and portfolios converge under their myopic probabilities. Diffusion models with several assets and a single state variable lead to the classic turnpike, in which optimal portfolios converge under the physical probability, and to the explicit turnpike, which identifies the limit of optimal portfolios in terms of the solution of an ergodic HJB equation. (Joint work with Kostas Kardaras, Scott Robertson, and Hao Xing)
 

Benedikt Blum (FAM @ TU Wien)
10:00, Besprechungsraum (Freihaus, 5th floor, green section)
Superreplication and Arbitrage in Multiasset Models under Proportional Transaction Costs (Ph.D. thesis presentation)

Antoine Jacquier (TU Berlin)
Implied volatility asymptotics in affine stochastic volatility models with jumps (close abstract)

Calibrating stochastic models is a fundamental issue on financial markets. The aim of this talk is to propose a calibration methodology based on the knowledge of the asymptotic behaviour of the implied volatility. We focus on the general class of affine stochastic volatility models with jumps, which encompasses the Heston (with jumps) model, exponential Levy models, the Barndorff-Nielsen and Shephard model. Under mild conditions on the jump measures, we derive (semi) closed-form formulae for the implied volatility as the maturity gets large.
 

PRisMa 2010
One-Day Workshop on Portfolio Risk Management
(FH HS 8 - Nöbauer Hörsaal, "Freihaus" Building of TU Wien)

Pasquale Cirillo (University Bern)
16:30, Freihaus Hörsaal 7 (Freihaus, 2nd floor, yellow section)
Firms' Size and Growth Rates - Some Econometric and Probabilistic Approaches (close abstract)

The study of Firms' size distribution (FSD) and growth processes has always had a great importance in industrial economics and statistics. Knowing how Firms are distributed and their degree of concentration on the market is indeed fundamental for the design of good policies. The same information is also very useful in courts when assessing and judging antitrust cases. Moreover from an econometric point of view, a deep understanding of the size distribution of Firms and how it is generated is for example essential for microsimulation purposes, view that FSD is a direct result of Firms' growth processes, market structure and economic interactions and constraints.
After a very short introduction about some basic empirical laws in industrial economics and statistics, such as Gibrat's law and Pareto-Laplace processes, I will give some results about the relationship between Firms' size and age. In particular, in the wake of other recent papers in the literature, I will show how FSD changes over time as Firms age, indicating different growth patterns for young and old companies. Using panel analysis I will further investigate the relationship between growth, age, size and profitability. Some results are still unpublished. In the second part of the talk I will focus on the upper tail of FSD, to investigate whether some Paretian behavior can be observed or not. For doing so I will use different statistical techniques, but also some tools coming from "econophysics".
All the empirical analyses are performed using Italian data from the CEBI industrial database.
In the last part of the talk, following my interest for combinatorial stochastic processes, I will finally sketch the basic characteristics of a still-indevelopment probabilistic model that, using a preferential attachment behavior, is able to generate a Pareto-Laplace process for Firms' dynamics, thus giving a possible theoretical explanation to the empirics discussed before.
 

Markus Fischer (Brown University, Rhode Island, USA)
Large deviation properties of weakly interacting Itô processes (close abstract)

Consider the following model for a system of N weakly interacting particles: N stochastic differential equations (SDEs) with coefficients all of the same functional form describe the state evolution of the particles; particles interact through the empirical measure of their states at any given time. In the diffusion case, it is known under certain conditions that the sequence of empirical measures converges, as N tends to infinity, to the weak solution of an associated McKean-Vlasov equation and that it satisfies a large deviation principle. We will present the derivation of a Laplace principle equivalent to the large deviation principle. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under mild assumptions and also for models described by SDEs not of diffusion type; to illustrate this, we present the case of SDEs with delay. (Joint work with Amarjit Budhiraja and Paul Dupuis)
 

Dirk Banholzer (TU München)
11.00
Intensitätsbasierte Kreditrisikomodelle (close abstract)

This talk deals with intensity-based credit risk models. The main aim is to provide a general overview of this kind of model class from a theoretical viewpoint, by explaining its fundamental concepts and methods and presenting some of the models which essentially have embossed its popularity.
After introducing the basic mathematical background for the intensity-based framework, the works of Jarrow and Turnbull (1995), Madan and Unal (1998), Lando (1998) and Duffie and Singleton (1999) are presented in greater detail, as these have mainly influenced the development of intensity-based models on a univariate obligor level.
With respect to modeling the defaults of multiple obligors, different possibilities to incorporate a dependency structure into the intensity-based setting are briefly discussed, before the most typical multivariate intensity-based approach of correlated intensities is specified. Latter approach serves as underlying framework to construct a simple bivariate intensitybased model for pricing credit default swaps when counterparty risk is present. The swap prices, which are obtained by realizing the model in an affine jump diffusion setting, are first compared to those created by an ordinary univariate approach. Subsequently, a sensitivity analysis is conducted in which the effects of changing single intensity parameters on the swap prices are examined.
 

Julia Eisenberg (University Cologne)
Optimal Control of Capital Injections by Reinsurance and Investments (close abstract)

We consider the classical continuous time risk model and its diffusion approximation. The claims are reinsured by some reinsurance. In addition to that the insurer is allowed to invest into a risky asset modeled as a Black-Scholes model. We choose as a risk measure the value of expected discounted capital injections, which are necessary to keep the risk process above zero. Our goal is to find the value function defined as the infimum of expected discounted capital injections over all reinsurance and investment strategies; and to derive the optimal strategy leading to the value function. We find an explicit expression for the value function and the optimal strategy in the case of diffusion approximation. In the classical risk model, we show the existence and uniqueness of a twice continuously differentiable solution to the Hamilton-Jacobi-Bellman equation under some special constraints. In the general case, we show the existence and uniqueness of the viscosity solution.
 

Alexander Hullmann (University Bonn)
17:00
The Generative Topographic Mapping for Dimensionality Reduction and Data Analysis (close abstract)

Most high-dimensional data exhibit some correlation structure, which means that points are not distributed uniformly in the data space. This usually leads to a low intrinsic dimension. The Principal Component Analysis is the best known method to find low-dimensional parametrisations of high-dimensional data. As it fails to capture non-linear dependencies, several more complex methods have been invented.
The Generative Topographic Mapping (GTM) is a method for non-linear dimensionality reduction, which has been published in 1998 by Bishop, Williams and Svensen. We will show how a continuous formulation of the GTM allows for efficient quadrature methods and discretisations, so that the 'curse of dimensionality' of the embedding dimension can be avoided to some extent.
We will use our modified GTM not only for dimensionality reduction but also for classification problems. This allows us to study the 'concentration of measure'-effects which can be observed when dealing with high-dimensional data.
 

Peter H. Gruber (Universitá Svizzera Italiana, Lugano)
13:30
Three Make a Dynamic Smile - Unspanned Skewness and Interacting Volatility Components in Option Valuation (close abstract)

We propose a new modeling approach to option valuation, in which the volatility and skewness of returns are functions of three distinct, but dependent, stochastic components: Two components modeling short and long run volatility risk and a third component capturing shocks to return skewness that are unspanned by shocks to volatility. The model state dynamics follows a matrix jump diffusion, provides efficient pricing formula for plain vanilla options and nests a number of existing multi-factor affine models. We introduce dynamic interactions between the different components by relating the persistence and local variance of the volatility factors to the degree of return skewness, and vice versa. We estimate our model using S&P 500 index option data. We find that models with unspanned skewness components and dynamic interactions provide better pricing performance and a more accurate description of the joint dynamics of the implied volatility surface, both in-sample and out-of-sample. These findings support the use of option pricing models with (i) at least three distinct components driving the volatility and skewness of returns, (ii) skewness components that are not completely spanned by volatility shocks and (iii) interactions between the distinct component dynamics. (Joint work with Claudio Tebaldi and Fabio Trojani)
 

Stefan Thonhauser (University Lausanne)
A randomized approach to analyzing the compound Poisson risk model under periodic observations (close abstract)

In the framework of the classical compound Poisson risk model, the idea of periodically balancing the books is introduced by randomizing the times at which the process is observed. Under the assumption that the inter-observation times are Erlang($n$) distributed, the model contains both the usual continuous-time and the discrete time risk models as limiting cases. We study the Gerber-Shiu function and expected discounted dividend payments via integro-differential equations as well as an alternative method using the discounted increments of the process. Numerical examples illustrate the effect of random observation times on various ruin-related quantities and the performance of the dividend strategy.
 

Markus Zahrnhofer (TU Graz)
9:30, Seminar room 101B ("Freihaus", green section, 3rd floor)
Modeling and pricing of temperature derivatives (close abstract)

Temperature has an essential influence on many business activities. A market for temperature derivatives in the US has emerged in the last decade. In Austria temperature derivative contracts are rare.
We consider mean-reverting Ornstein-Uhlenbeck processes with different volatility functions for modeling the dynamics of temperature. Further we present a pricing method for temperature derivatives which is based on the mean-reverting Ornstein-Uhlenbeck process. We use the risk neutral pricing approach for analysing futures and options written on different temperature indices.
Based on these pricing formulas we give an improvement for firms, which are exposed to temperature at various sites simultaneously. We introduce a continuous spatial-temporal model to construct an optimal portfolio which reflects the need of a company optimally.
 

Klaus D. Schmidt (Technische Universität Dresden)
12:00
Markov-Ketten und Bonus-Malus Systeme (close abstract)

In der Schadenversicherung stellen Bonus-Malus Systeme ein verbreitetes Mittel zur Prämiendifferenzierung und zur Risikoselektion dar.
Der Vortrag zeigt, wie sich der Folge der jährlichen Schadenzahlen zunächst eine Markov-Kette und sodann ein Bonus-Malus System konstruieren lässt, in dem das Prämienniveau von der erreichten Bonus-Malus Klasse abhängt. Dabei kann unter Verwendung Bayes'scher Methoden auch die Inhomogenität des Bestandes modelliert und eine Risikoselektion erreicht werden.
 

Klaus D. Schmidt (Technische Universität Dresden)
16:30, Freihaus Hörsaal 4 (Freihaus, 2nd floor, yellow section)
Lineare Modelle in der Schadenreservierung: Korrelation, Prognose, und Prognosefehler
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Karl F. Bannör (Frankfurt/Main)
9.30-11.00, Seminar room 101C
The Longstaff-Schwartz approach to the optimal stopping problem (close abstract)

Many option-type claims have an early exercise feature, for their evaluation an optimal exercise strategy has to be determined. In practice this strategy is often calculated by backward induction. Here the calculation of a conditional expectation is the usual obstacle. Longstaff and Schwartz introduced an elegant method founded on basic results from Hilbert space theory how to implement a backward induction algorithm. This algorithm can be embedded in a Monte-Carlo simulation framework and is widely used in practice for the evaluation of Bermudan or American style claims. In my talk I will present the foundations and ideas of Longstaff's and Schwartz's results and show some tricks for implementing it from a practitioner's view.
 

David Millar (Chief Operating Officer PRMIA), Stefan Strehle and Christoph Obenhuber (PRM degree holders)
18.30-20.00, FH Hörsaal 8 "Nöbauer" (Freihaus, 2nd floor, yellow section)
PRMIA Education and Exam Information (close abstract)

The financial crisis has demonstrated the need for sound risk management practices in the (financial) industry. As risk managers must have a profound knowledge of state of the art risk management tools and methods, corresponding educations programs are needed.
PRMIA (Professional Risk Managers' International Association) is a non-profit professional association offering access to a broad spectrum of resources to its members. The PRM Certification - which is endorsed by leading universities and businesses - is a global standard for financial risk managers, and is offered in 140 countries. The presentation gives information about the PRMIA exams (PRM and Associate PRM) and you can hear from individuals who have already passed them, including some more detailed information and practical advice on the exams.
Following the official event you will have the opportunity to socialize with other attendees from the Austrian risk management and banking community.
PRMIA-Einladung (Anmeldung nicht erforderlich)
 

Dilip Madan (University of Maryland, USA)
Unlimited Liabilities, Reserve Capital Requirements and the Taxpayer Put Option (close abstract)

When firms access unbounded liability exposures and are granted limited liability, then an all equity firm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve capital at stake in the firm. We contribute by (i) valuing this taxpayer put, and (ii) determining the level for reserve capital. Reserve capital levels are designed to mitigate the adverse incentives for unnecessary risk introduced by the taxpayer put at the firm level. In our approach, the level of reserve capital is set to make the aggregate risk of the firm externally acceptable, where the specific form of acceptability employed is positive expectation under a concave distortion of the cash flow distribution. It is observed that in the presence of the taxpayer put, debt holders may not be relied upon to monitor risk as their interests are partially aligned with equity holders by participating in the taxpayer put. Further, it leads to an equity pricing model associated with a market discipline that punishes perceived cash shortfalls.
 

Gregory Temnov (University College Cork, Ireland)
Extended stability property for exponential families: a model for financial applications (close abstract)

A class of distributions originating from an exponential family and having a property related to the strict stability is described. An explicit form for the characteristic function is given. It appears that the resulting class coincides with a subclass of Tweedie distributions, respectively it is related to stable distributions and includes Inverse Gaussian distribution and Levy distribution as special cases. Due to its origin, the proposed distribution has a sufficient statistic. Besides, it combines stability property at lower scales with an exponential decay of the distribution's tail and has an additional flexibility due to the convenient parameterization. All of it provides a motivation for using the proposed class in financial modelling. Apart from the basic model, we consider a generalization related to geometric stable distributions.
 

Robert Stelzer (TU München)
16:30, Seminar Room 101C (Freihaus, 4th floor, green section)
Derivative Pricing and Long Memory in the Multivariate Ornstein-Uhlenbeck type Stochastic Volatility Model (close abstract)

In this talk we consider a multivariate stochastic volatility model for financial assets based on positive semi-definite Ornstein-Uhlenbeck type processes. First we discuss the pricing of financial derivatives in this model focusing especially on pricing via Laplace transforms and we show that calibration to observed prices becomes very feasible when choosing appropriate parametric assumptions. We illustrate this with a data example from foreign exchange markets. In the second part of the talk we consider an extension of the model allowing to capture long range dependence in the squared returns. To this end we introduce supOU processes defined in terms of a Levy basis (or infinitely divisible independently scattered random measure). After analysing some of their properties, we look at the implications of using them as the instantaneous covariance matrix processes in a stochastic volatility model.
 

Gernot Müller (TU München)
Statistical Aspects of COGARCH Modelling (close abstract)

The COGARCH model has been introduced by Klüppelberg et al. (2004) as a continuous-time analogue of the well-known discrete-time GARCH model. It preserves many features of GARCH, in particular it incorporates only one source of uncertainty, since it is driven by a single univariate Levy process.
In this talk we first recall some statistical properties of the COGARCH model and discuss several methods for estimation. In particular, we summarize some results on the relations between GARCH and COGARCH. Next we apply the COGARCH model to daily data from the S&P 500 in order to investigate Merton's hypothesis on the risk-return tradeoff. In the last past, we propose an asymptotic test for the special feature of COGARCH, that there is a fixed functional relationship between the jumps of the log-price process and the jumps of the corresponding volatility process. The test uses local volatility estimates calculated from observation windows before and after the jumps under consideration. We assess the finite sample behavior of the proposed test in a simulation study.
 

Stefan Gerhold (FAM @ TU Wien)
Refined volatility expansion in the Heston model (close abstract)

It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes (Roger Lee's moment formula). Motivated by recent tail-wing refinements of this moment formula, we first derive a novel tail expansion for the Heston density, and then show the validity of a refined volatility expansion. Our methods and results may prove useful beyond the Heston model: the entire analysis is based on affine principles; at no point do we need knowledge of the (explicit, but cumbersome) closed form expression of the Fourier transform of log-spot. This is joint work with P. Friz, A. Gulisashvili, and S. Sturm.
 

Katja Krol (Humboldt University, Berlin)
Minimal Entropy Martingale Measure for Lévy Processes (close abstract)

In this talk we consider the problem of minimization of the relative entropy process among all equivalent martingale measures for a real-valued Lévy process X. We show that the known sufficient conditions for the existence of the minimal entropy martingale measure P^MEMM are also necessary, which provides a complete characterisation of P^MEMM and the entropy process. We also demonstrate the connection to the Esscher martingale transform for exponential Lévy processes, which have a wide application in mathematical finance.
This talk is based on a joint work with Uwe Küchler.
 

Praxis der Finanz- und Versicherungsmathematik 2010
Montag, 1. März bis Dienstag, 2. März 2010, jeweils ca. 9-17 Uhr
TU Wien, details

Praxis der Finanz- und Versicherungsmathematik 2010
Montag, 1. März bis Dienstag, 2. März 2010, jeweils ca. 9-17 Uhr
TU Wien, details

Habib Esmaeili (TU München und WPI)
Parameter estimation of Levy copula-based models with application in insurance (close abstract)

In this talk we study a bivariate compound Poisson process (CPP) with dependence structure modeled by a Levy copula. With an example in insurance, we show the the application of such models. We consider a parametric model for the Levy copula and estimate the parameters of a full dependent model based on a maximum likelihood approach. This approach can be generalized to the Levy processes with some restrictions on the observation scheme. As observation scheme we assume that we observe all jumps larger than some epsilon >0 and base our statistical analysis on the resulting CPP. We derive the Fisher information matrix for a bivariate Stable process and and prove asymptotic normality of the estimates when the number of jumps tends to infinity. A simulation study investigates the loss of efficiency because of the truncation. Finally we will introduce the two-step estimation procedure where we estimate the parameters of the marginal processes in first step and the parameters of the dependence structure in the second step.
 

Eberhard Mayerhofer (Vienna Institute of Finance)
On strong solutions of positive definite jump-diffusions (close abstract)

We show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes. Joint work with R. Stelzer and O. Pfaffel, TU Munich.
 

Pavel V. Shevchenko (CSIRO Mathematical and Information Sciences, Sydney)
16:30, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
Quantitative modelling of financial risks
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

László Györfi (Budapest University of Technology and Economics)
Portfolio games (close abstract)

The growth optimal investment strategies are based on three principles:

• log-optimal rebalancing
• nonparametric estimates
• machine learning algorithms

In this talk we illustrate the rebalancing for the Kelly games, for the horse racing and for the St. Petersburg games.
 

Cordelia Rudolph (LMU München)
Gegenseitige Abhängigkeit von Ausfällen in Modellen mit Intensitäten (close abstract)

Kreditderivate und Ausfälle von Vertragsteilnehmern werden häufig in sogenannten Standardmodellen, die auf Cox Prozesse und deren Intensitäten zurückgreifen, analysiert. Allerdings ist die Berechnung der Sprünge eines Cox Prozesses sehr rechenintensiv, da Monte Carlo Simulationen erforderlich sind. Alternativ ist es möglich, Kreditderivate oder Ausfälle als einen affinen Prozess zu betrachten. Hat man den zugehörigen infinitesimalen Generator spezifiziert, hängt die Berechnung z.B. eines Ausfalles nur von der Lösung eines Systems gewöhnlicher Differentialgleichungen ab.
Diese zwei Ansätze betrachten wir anhand eines Credit Default Swaps (CDS). Es birgt auch die Möglichkeit, untereinander abhängige Ausfälle zu untersuchen. Dazu führen wir ein Intensitätenmodell ein, das auf Cox Prozessen basiert. Der Preis des CDS wird mit der Monte Carlo Methode simuliert. Des Weiteren führen wir ein Intensitätenmodell ein, das auf affinen Prozessen aufbaut. Wir betrachten verschiedene Kalibrierungen dieses Modells und vergleichen die Berechnung des CDS Preises mit der Approximation durch das Intensitätenmodell mit Cox Prozessen. Aus verschiedenen Gründen weisen diese beiden Lösungsansätze für das Problem unterschiedliche Ergebnisse vor.
 

Paolo Guasoni (Boston University and Dublin City University)
12:00
The Incentives of Hedge Fund Fees and High-Water Marks (close abstract)

Hedge fund managers receive a large fraction of funds' profits, in addition to a regular fee proportional to the the funds' assets, which is typical of mutual funds. The additional fee is paid only when the fund exceeds its previous maximum - the high-water mark.
To understand the incentives implied by this fees, we solve the problem of a manager with Constant Relative Risk Aversion and a Long Horizon, who maximizes the terminal utility from future fees.
With constant investment opportunities, the manager's optimal portfolio is constant for typical levels of risk aversion. It coincides with the portfolio of an investor with a different risk aversion, which depends on the manager's risk aversion and on the size of the fee. This portfolio is also related to that of an investor with a drawdown constraint.
The model involves a stochastic differential equation involving the running maximum of the solution, which is related to perturbed Brownian Motions. The solution of the control problem uses a verification theorem which relies on asymptotic properties of positive local martingales.
 

Mark Podolskij (ETH Zürich)
13:30 Böcklsaal (Karlsplatz 13, Main Building, 1st floor)
Statistische Methoden für hochfrequente Beobachtungen von Semimartingalen (close abstract)

In diesem Vortrag werden die wichtigsten Methoden für die statistische Analyse von Hochfrequenzdaten von Semimartingalen dargestellt. Semimartingale treten als natürliche Modelle für Preisprozesse auf (unter der sogenannten No-Arbitrage-Annahme). Gegeben hochfrequente Beobachtungen auf einem festen Intervall, ist man typischerweise an der Schätzung bestimmter Charakteristika (quadratische Variation, Sprünge usw.) eines Semimartingals interessiert. Ich präsentiere die wichtigsten Methoden für die obigen Schätzprobleme, darunter die klassische Power Variation (bzw. Multipower Variation) und die trunkierte Power Variation. Es werden die Konsistenz und einige zentrale Grenzwertsätze dargestellt. Abschliessend werden Modelle mit Marktmikrostruktureffekten behandelt.
 

Thorsten Schmidt (TU Chemnitz)
10:00, Böcklsaal (Karlsplatz 13, Main Building, 1st floor)
Die Modellierung von Portfolio-Kreditrisiken (close abstract)

Der Vortrag beschäftigt sich mit der Modellierung von Portofio-Kreditrisiken und der Bewertung von Collateralized Debt Obligations (CDOs). Neben der Betrachtung allgemeiner, dynamischer Modellierungsmöglichkeiten wird auch auf die statistische Problematik sowie auf die Herleitung von Absicherungsstrategien Wert gelegt.
 

Sylvia Frühwirth-Schnatter (Universität Linz)
16:15
Modellierung multivariater Finanzzeitreihen mittels multidimensionaler zeitstetiger Markov Switching Modelle (close abstract)

Thema des Vortrags ist die gemeinsame Modellierung multivariater Finanzzeitreihen mittels eines multivariatenDiffusionsprozesses, bei dem sowohl der Driftvektor als auch die Volatiltitätsmatrix nicht fix sind, sondern von einer latenten zeitstetigen Markovkette mit endlich vielen Zuständen abhängen.
Unbekannte Parameter dieses Modells sind die Anzahl der Zustände der latenten Markov-Kette, deren Intensitätsmatrix sowie der Driftvektor und die Volatiltitätsmatrix des Diffusionsprozesses in den verschiedenen Zuständen. Verschiedene Methoden zur ökonometrische Schätzung der Parameter dieses zeitstetigen Modells aus diskreten Beobachtungen werden vorgestellt und miteinander verglichen. Für simulierte Beobachtungen zeigt sich, dass eine Bayesianische Schätzung unter Verwendung von Markov Ketten Simulationsmethoden (MCMC) bessere Ergebnisse liefert als eine klassische Maximum Likelihood Schätzung.
Abschließend wird die Anwendung dieses multidimensionalen zeitstetigen Markov Switching Modells auf die simultane Modellierung von 4 amerikanischen Aktienindices (Argentinien, Brasilien, Mexiko, USA) demonstriert. Unter Verwendung des BIC (Bayesian Information Criterion) wird ein Modell mit 4 Zuständen identifiziert. Eine Analyse der geschätzten Parameter zeigt neben der zu erwartenden Veränderung der Volatilität der einzelnen Indices in den einzelnen Zuständen auch eine Veränderung der Korrelation zwischen den Indices.
 

Jan Kallsen (Universität Kiel)
14:00
Zur Modellierung von Optionspreisflächen (close abstract)

Der Heath-Jarrow-Morton-Ansatz (HJM) in der Zinstheorie geht nicht vom kurzfristigen Zins aus, sondern betrachtet die gesamte Forward-Rate-Kurve als Gegenstand der stochastischen Modellierung. Die Anforderung der Arbitragefreiheit führt dann zu Konsistenz- und Driftbedingungen, insbesondere der Heath-Jarrow-Morton-Driftbedingung.
Es wurden in jüngerer Zeit einige Anstrengungen unternommen, um diese Idee auf Aktienoptionen zu übertragen, siehe etwa Schönbucher (1999), Schweizer und Wissel (2008), Carmona und Nadtochiy (2009), Jacod und Protter (2006). Die Rolle des kurzfristigen Zinses wird hier von der zugrunde liegenden Aktie übernommen. Die implizite Volatilitätsfläche oder eine geeignete Reparametrisierung dienen als Gegenstück der Forward-Rate-Kurve in der klassischen HJM-Theorie.
In diesem Vortrag wird ein neuer Ansatz zur Modellierung impliziter Volatilitätsflächen vorgeschlagen, der dem von Carmona und Nadtochiy (2009) dahingehend ähnelt, dass die zentralen Merkmale eines HJM-Ansatzes erhalten bleiben. Er basiert jedoch auf einer anderen Parametrisierung, was sowohl die Theorie als auch deren Anwendung erleichtert.
 

Rüdiger Frey (Universität Leipzig)
10:30
Innovation: Pricing and Hedging of Credit Derivatives via the Innovations Approach to Nonlinear Filtering (close abstract)

After a brief introduction to credit risk modeling and credit derivatives we propose a new, information-based approach for modeling the dynamic evolution of a portfolio of credit risky securities. In our setup market prices of traded credit derivatives are given by the solution of a nonlinear filtering problem. The innovations approach to nonlinear filtering is used to solve this problem and to derive the dynamics of market prices. Moreover, the practical application of the model is discussed: we analyze model calibration, the pricing of exotic credit derivatives and the computation of risk-minimizing hedging strategies. The talk closes with a small numerical case study.
 

Giovanni Cesari (UBS Investmentbank London, UK)
16:30, Freihaus Hörsaal 3 (Freihaus, 2nd floor, yellow section)
Modelling, Pricing, and Hedging Counterparty Credit Exposure
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Wolfgang Runggaldier (Università degli Studi di Padova, Italy)
Pricing under incomplete information without equivalent martingale measures (close abstract)

Market diversity may, among other things, give rise to arbitrage opportunities and this in turn implies that quantities, which in traditional theory are martingales, are then strict local martingales. It was shown in an approach followed by Fernholz, Karatzas and Kardaras that availability of only local martingales need not preclude option pricing and hedging. On the other hand, using benchmarking with respect to the growth optimal portfolio, Platen derived an approach that leads to pricing in terms of expectations under the physical measure, independently on whether a martingale measure exists or not. In the paper we consider the above two approaches in the context of partial information on the market model and show that, for pricing, they lead to the same results not only under complete, but also incomplete information. (Based on joint work with Giorgia Galesso).
 

Martin Schweizer (ETH Zürich, Switzerland)
10:30, Hörsaal 4 Hochstetter (Karlsplatz 13, Main Building, Hof 1, ground floor)
Horizon-dependence in optimal portfolio choice (close abstract)

Let us consider the standard problem of maximising expected utility from terminal wealth over self-financing strategies, with a utility function which is also allowed to depend on time and omega. For each fixed T, denote by X_T the optimal terminal wealth for the problem with time horizon T. This means that each X_T is a stochastic integral of the underlying price process S - but of course the integrand (which is the optimal portfolio for the time horizon T) depends on T. Now consider the collection X_T (for T>0) of these random variables as a stochastic process. What kind of process is this, and what is its structure? Understanding this question is crucial for understanding how optimal portfolio choice depends on the time horizon. Answering this question also brings up other challenging mathematical problems in a natural way.

The results given in this talk are joint work with Tahir Choulli (University of Alberta, Edmonton, Canada).
 

Mario Wüthrich (ETH Zürich, Switzerland)
16:30, HS 7 Schütte-Lihotzky (Karlsplatz 13, Main Building, Stiege 7, ground floor)
Modellierung des Abwicklungsergebnisses im neuen Solvenz-Modell (Slides)
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

PRisMa 2009
One-Day Workshop on Portfolio Risk Management

Hannes Kazianka (Alpen-Adria Universität Klagenfurt, Austria)
16:30, SEM 107
Copula-based geostatistical modeling and interpolation (close abstract)

Common spatial models rely on the assumption of a Gaussian random field which is not fulfilled for environmental processes. In our work we propose the use of copulas to describe the spatial variability and to deal with non-Gaussianity.

We show how location dependent covariates e.g. a spatial trend can be accounted for in spatial copula models. Furthermore, we introduce geostatistical copula-based models that are able to deal with random fields having discrete marginal distributions. When using the Gaussian copula we propose a Bayesian model where the priors for the parameters of the correlation structure are chosen in an objective Bayesian way. In the absence of analytical expressions for the joint posterior we use a Metropolis algorithm to obtain posterior samples.

We present methods for copula-based spatial interpolation and explain their advantages over classical approaches to spatial prediction. Finally, we illustrate our methodology by analyzing two non-Gaussian data sets that contain extreme measurements.
 

Carlo Sgarra (Politecnico di Milano, Italy)
Risk premium and risk-neutral valuation in electricity markets (close abstract)

In Electricity Markets the Risk Premium associated with Forward prices enjoies a peculiar property: it can change sign between short and longer maturities. This phenomenon has been systematically observed and thorougly investigated by an econometric viewpoint. In this talk we are going to provide a theoretical justification of the risk premium sign change on the basis of the most popular models available in the literature and of the most natural probability measure change: the Esscher Transform. In the framework of spot price dynamics described by Independent Increment processes we shall show that a measure change performed via the Esscher Transform can justify the sign change of the risk premium between short and longer maturities.
This talk is based on a joint work with F.E. Benth of the C.M.A. (center of Mathematics for Applications) of the Oslo University
 

Antonis Papapantoleon (Quantitative Products Laboratory, Berlin, Germany)
Towards an "affine LIBOR" model with default risk (close abstract)

I will discuss some ongoing work with Zorana Grbac (Univ. Freiburg) about the modeling of defaultable LIBOR rates in the spirit of the "affine LIBOR" model.
 

Laura Ballotta (City University London, UK)
Investment strategies and risk management for participating life insurance contracts (close abstract)

(by Laura Ballotta and Steven Haberman)

This paper proposes an asset allocation strategy for the risk management of the broad category of participating life insurance policies. The nature of the liability implied by these contracts allows us to treat them as options written on the reference portfolio backing the policy; consequently, the valuation approach is based on classical contingent claim theory. This leads to the identification of additional safety loadings against the risk of default implied by these contracts, and the setting up of suitable investment strategies aimed at minimizing this risk. The impact on the solvency requirements for the capital of the insurer of the proposed asset allocation strategy is analyzed by means of Monte Carlo techniques. Stress testing is considered as well with respect to the key risk factors of the model, such as the equity volatility and the market interest rate. The numerical analysis shows that, for the specific policy design considered in this paper, a suitable choice of the participation rate combined with the proposed investment strategy minimizes the overall default risk of the insurance company, both in terms of probability of default and expected severity. Keywords: asset allocation, fair valuation, Monte Carlo methods, participating contracts, solvency requirements, TVaR.
 

Andrea Pascucci (University of Bologna, Italy)
Kolmogorov equations and applications to path dependent derivatives (close abstract)

The talk presents a survey of the theory of partial differential equations of Kolmogorov type and the related diffusion processes arising in physics and in mathematical finance.

These evolutionary PDEs, which are generally non-uniformly parabolic, are naturally associated to stochastic models with memory. Financial derivatives with dependence on the past provide some typical examples. Asian options of European and American style and the modeling of stochastic volatility for the evaluation of derivative securities will be discussed.
 

6. TU-Forum: F.X. Hof, U. Schmock u. J. Teichmann
18:00, Prechtl-Saal der TU Wien (Stiege 1/EG, 1040 Wien, Karlsplatz 13)
Wirtschafts- und Finanzkrise: Woher kommt sie? Wohin kann sie führen? (close abstract)

Längst ist von der Krise nicht mehr nur der Finanzsektor betroffen: Industrieumsätze sinken und Arbeitslosenzahlen steigen. Wie konnte es zu so einer dramatischen Situation kommen? Wie entstehen und platzen Spekulationsblasen? Wie funktionieren die komplexen Finanzderivate, die das ermöglichen? Wie geht es weiter, und welche Strategien gibt es, um aus der Krise wieder herauszukommen?

Über solche und ähnliche Fragen sprechen beim sechsten TU Forum
Prof. Franz X. Hof, Forschungsgruppe für Ökonomie,
Prof. Uwe Schmock, Forschungsgruppe für Finanz- und Versicherungsmathematik
und Prof. Josef Teichmann, Forschungsgruppe für Finanz- und Versicherungsmathematik

Die Veranstaltung findet am 19. Mai 2009 um 18:00 im Prechtl-Saal der Technischen Universität Wien (Stiege 1/EG, 1040 Wien, Karlsplatz 13) statt. Moderator der Veranstaltung ist Christian Müller, Wissenschaftsredakteur der Austria Presse Agentur.

Die Technische Universität (TU) Wien stellt sich ihrer gesellschaftlichen Verantwortung und greift in der Reihe "TU-Forum" Themen mit technischem Hintergrund auf, die polarisieren.

Der Eintritt ist frei - die TU Wien freut sich auf Ihren Besuch!
 

Ronnie Loeffen (Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria)
De Finetti′s dividend problem with absolutely continuous controls (close abstract)

In this talk we take a look at an offshoot of de Finetti′s dividend problem for Lévy processes with no upward jumps. Namely, we consider the version of the control problem in which the dividend strategies are assumed to have a density which is uniformly bounded by a constant. We look for conditions on either the jump measure or on the scale function of the Lévy process, that guarantee that a certain simple bang-bang policy forms the optimal dividend strategy. The main difficulty lies in handling the convolution term appearing in the value function of such a strategy.
 

Anja Richter (Humboldt University Berlin, Germany)
Differentiablity of quadratic BSDEs driven by continuous martingales (close abstract)

We consider quadratic growth Backward Stochastic Differential Equations (BSDEs) driven by continuous local martingales. First we establish the differentiability of a FBSDE with respect to the initial value of its forward component. Then we derive the Markov property of the forward-backward system when the driving martingale is a strong Markov process. This allows us to derive the control process of the BSDE in terms of a differential operator of the solution process and the correlation coefficient of the forward process. This representation generalizes the results obtained in the Brownian setting involving the Malliavin calculus which is not available in the general martingale setting. Consequently, we propose a new method based on stochastic calculus techniques.
 

Sasa Parad (ETH Zürich, Switzerland)
17:00
Long Run Asset Prices with General Utilities (close abstract)

We perform a detailed asymptotic analysis of equilibrium behavior of asset prices, wealth size and portfolio weights in complete markets equilibria, with long-lived funds.
In equilibrium, the fund with the (closest to) log preferences will dominate other funds in size, in the longrun, with probability one. On the other hand, two funds on the opposite sides of the log preference will never dominate each other in expected size.

In the very long run, the price behavior of the risky asset will be determined solely by the fund closest to the log preference. However, surprisingly, the price drift and volatility still are affected by higher risk aversions, and optimal portfolio weights contain a hedging component, positive (negative) for risk aversion higher (lower) than log. For earlier, but still asymptotically infinite times, the price behavior is also impacted by the funds whose risk aversions are greater than one
 

Dejan Veluscek (FAM, TU Vienna)
16:00
Higher order weak approximation schemes for SDEs (close abstract)

Weak approximation schemes for SDEs are frequently used probabilistic methods for numerical calculation of E(f(X(T,x)), where X(T,x) is a solution of a given SDE at time T with initial value x. Weak approximation schemes play an important role in mathematical finance, since the price of a financial derivative written on the diffusion X(t, x) is obtained by the calculation of E[f(X(T, x))].
The talk will present a survey on several recent higher order weak approximation schemes for SDEs which share the property of having an "algebraic background", e.g. the cubatures (Lyons, Victoir 2004 ), N-V approximation scheme (Ninomiya, Victoir 2008), N-N approximation scheme (Ninomiya, Ninomiya 2009).
Under suitable conditions on function f and on vector fields that drive the underlying SDE there exists an expansion of the error term. The talk will present several extrapolation techniques that use this fact to "kill" additional error terms and thus raise the order of the mentioned weak approximation schemes.
 

Vicky Henderson (Oxford-Man Institute of Quantitative Finance, UK)
Prospect Theory, Partial Liquidation and the Disposition Effect (close abstract)

We solve a liquidation problem for an agent with prospect theory preferences who seeks to sell a portfolio of (divisible) claims on an underlying asset. Our methodology enables us to consider different formulations of prospect preferences in the literature, and various asset price processes. We find that these differences in specification are important - for instance, with piecewise power functions (but not piecewise exponentials) the agent may voluntarily liquidate at a loss relative to break-even. Further, we find that the likelihood of liquidating at a (small) gain is much higher than liquidating at a (large) loss, consistent with the disposition effect documented in empirical and experimental studies. The ability to partially liquidate also has significant consequences.
 

Stephan Sturm (TU Berlin, Germany)
A General Approach to Small-Time Large Deviations for Sample Paths of Infinite Dimensional Symmetric Dirichlet Processes with Applications to the Wasserstein Diffusion (close abstract)

Symmetric diffusions on a Polish space can be characterized via local, quasi-regular symmetric Dirichlet forms. We define a suitable pointwise intrinsic metric associated to the Dirichlet form which allows us to introduce the notion of energy (with respect to this intrinsic metric) of a sample path. Under mild assumptions – which imply the necessary exponential tightness – we prove a general small-time sample path large deviation principle for diffusions on a Polish space.

As concrete application of this general approach we derive the small time large deviations for the Wasserstein diffusion on the space of probability measures on the unit interval.
 

Mia Hinnerich (Aarhus University, Denmark)
Inflation-indexed swaps and swaptions (Slides) (close abstract)

The article considers the pricing and hedging of inflation-indexed swaps, and the pricing of inflation-indexed swaptions, and options on inflation-indexed bonds. To price the inflation-indexed swaps, we suggest an extended HJM model.
The model allows both the forward rates and the consumer price index to be driven, not only by a standard multidimensional Wiener process but also by a general marked point process. Our model is an extension of the HJM approach proposed by Jarrow and Yildirim (2003) and later also used by Mercurio (2005) to price inflation-indexed swaps. Furthermore we price options on so called TIPS-bonds assuming the model is purely Wiener driven. We then introduce an inflation swap market model to price inflation-indexed swaptions. All prices derived have explicit closed-form solutions.
Furthermore, we formally prove the validity of the so called foreign-currency analogy.
 

Gregory Temnov (University College of Dublin, Ireland)
Analysis of limit distributions in actuarial modelling (close abstract)

In the analysis of actuarial data, useful approximations are often based on the assumption that the data is independent and identically distributed (iid), while the real data usually deviates from iid assumption.
We investigate the effects of such deviations on the results of parameters’ estimates in mis-specified models. In the same context, we investigate families of distributions such as Stable and Generalized Pareto distributions used as limiting models for both actuarial and financial data and propose some alternative representations with generalized properties. Besides, we discuss the optimization of numerical techniques for fitting and for the aggregation of the empirical data, which is also associated with actuarial applications.
 

Nikos Sfakianakis (Wolfgang Pauli-Institute, Vienna)
Adaptive mesh reconstruction and TVB for Hyperbolic Conservation Laws (close abstract)

Numerical treatment of PDEs often results to unphysical instabilities. We address this problem for Conservation Laws resolved by Finite Difference or Finite Volume numerical schemes.
In this regime the instabilities are due to the dispersive, the anti-diffusive or even the non-entropic nature of the numerical schemes and they are depicted either as wild oscillations or as entropy violating rarefaction waves.

In this talk we discuss and analyse a non-uniform mesh reconstruction procedure able to tame these instabilities. We provide numerical results and we prove that proper mesh reconstruction provides a bound on the Total Variation of the numerical solution. Moreover we prove that the variation increase due to oscillations can decrease; yielding a Total Variation Increase Diminishing scheme.
 

Hanspeter Schmidli (University of Cologne, Germany)
16:30, Freihaus Hörsaal 5 (Freihaus, 2nd floor, green section)
On Optimal Dividends and Capital Injections in Risk Theory
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Eberhard Mayerhofer (Vienna Institute of Finance)
Affine Diffusion Processes: Theory and Applications (close abstract)

I report on a recent work with Damir Filipovic on affine diffusion processes on canonical state-spaces.

In the corresponding article, a detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions and provide a full proof of existence and uniqueness through stochastic invariance of the canonical state space. Existence of exponential moments and the full range of validity of the affine transform formula are established. This is applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models.
 

Peter K. Friz (University of Cambridge, UK)
16:00
Minicourse on Stochastic Analysis via Rough Paths (Last of three parts)

Peter K. Friz (University of Cambridge, UK)
16:00
Minicourse on Stochastic Analysis via Rough Paths (Second of three parts)

Johannes Muhle-Karbe (TU Munich, Germany)
14:30
On asymptotic power utility-based pricing and hedging (close abstract)

Kramkov and Sîrbu (2006, 2007) have shown that in incomplete markets, first-order approximations of utility-based prices and hedging strategies markets cab be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and relative to a suitable numeraire. To facilitate computations, we propose an alternative representation in terms of the original numeraire.

In the second part of the talk, we discuss how to apply these results in affine models allowing for both jumps and stochastic volatility. Using results on affine semimartingales and mean-variance hedging, we show how the relevant quantities can be represented in semi-explicit form. Moreover, we present some numerical results for the model of Barndorff-Nielsen and Shephard (2001).
 

Mirta Castro Smirnova (Universidad de Sevilla, Spain)
Matrix valued orthogonal polynomials satisfying differential equations (close abstract)

Consider a risk process X&subt, which can either be a classical risk model or a diffusion approximation. The investors can choose the accumulated \emph{dividend process} {D_t} and/or the accumulated capital injection process {Z_t}. These two processes should be increasing cadlag processes. The goal is to find the optimal strategy maximising the discounted expected value of the dividends minus the penalised expected discounted value of the injections. We give the corresponding Hamilton--Jacobi--Bellman equation, from which the value function and the optimal strategy can be calculated.
 

Josef Teichmann, Antonis Papapantoleon, Martin Keller-Ressel (START-Prize Group, Vienna University of Technology)
A new approach to LIBOR modeling (close abstract)

LIBOR market models for interest rate derivatives suffer from severe intractability problems due to the random terms that enter the SDEs during the construction of the model. As a result, if the driving process is continuous then caplets can be priced in closed form, but not swaptions or other multi-LIBOR products; in case the driving process has jumps, then even caplets cannot be priced in closed form. In both cases, the calibration of the model to cap and swaption market data is very difficult and requires some short of approximation ("frozen drift" approximation). On the other hand, modeling forward prices produces a very tractable model, but negative LIBOR rates can occur, which contradicts any economic intuition.

In this work we propose a new approach to modeling LIBOR rates based on affine processes. We construct martingales that stay greater than one for all times, utilizing the Markov property of affine processes. Then, we model LIBOR rates in a framework that produces positive LIBOR rates in an analytically tractable model. In particular, closed form valuation formulas - using Fourier transforms - for caplets and swaptions are derived, hence the calibration of the model is very easy.
 

Angelika May (Universität Oldenburg, Germany)
16:30, Zeichensaal 3 (Freihaus, 7th floor, green section)
CPPI Models for life insurance products with guarantees
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Peter K. Friz (University of Cambridge, UK)
16:00
Minicourse on Stochastic Analysis via Rough Paths (First of three parts)

Martin Keller-Ressel (Financial and Actuarial Mathematics, Vienna University of Technology)
13:00, Seminar room 101C
Defense Talk: Affine Processes - Theory and Applications in Finance (close abstract)

The class of affine processes has been introduced by Duffie, Filipovic and Schachermayer, and consists of all continuous-time Markov processes, whose log-characteristic function depends in an affine way on the initial state vector of the process. In the first part of the thesis we show that any affine process is also a Feller process. We give an alternative proof for the main result of Duffie et. al. under an additional regularity condition, the class of affine processes can be completely characterized in terms of the infinitesimal generator, and the characteristic function of the process satisfies an ODE of the generalized Riccati type.

Subsequently we introduce two sufficient conditions for regularity. The second of these conditions defines a subclass of affine processes, that we call 'analytic affine'. These processes have the property that the generalized Riccati equations can be analytically extended to a subset of the real numbers, where they describe the time-evolution of moments and cumulants of the process. Finally we show that the operations of projection, time-integration, exponential change of measure, and subordination of an independent L\'{e}vy process all preserve the affine property. In the second part of the thesis we turn towards applications of affine processes to the modelling of stochastic volatility. We define the class of 'affine stochastic volatility models' (ASVMs), which includes a multitude of stochastic volatility models that have been proposed in the literature, including the Heston model, the models of Bates (1996 and 2000), and the Barndorff-Nielsen-Shephard model.

We derive results on the long-term behavior of an ASVM, and study moment explosions of the price process. We conclude with a discussion of possible applications of these results, for example to derive asymptotics of the implied volatility surface.
 

Jose Fajardo (IBMEC Business School, Rio de Janeiro)
Optimal Insider Strategy with Penalties (close abstract)

We study the optimal trading strategy of an insider who is subject to the possibility of law penalties due to his or her illegal trading activity. This possibility was absent in previous works. Also, we study the optimal penalty level that a regulator must applied in order to maximize a social welfare function.
 

Juan Pablo Ortega (CNRS, Dept. de Mathématiques de Besançon, France)
GARCH pricing via local risk minimization (close abstract)

GARCH is a parametric family of time series models that has been very successful in reproducing various features (leptokurtosis, volatility clustering,...) that are empirically observed in the distributions and in the dynamics of the returns associated to stock prices, currency exchange rates, or prices of certain commodities. The pricing of derivative products whose underlying asset is modeled using GARCH is not straightforward since the associated market is incomplete and hence perfect replication using a self-financing portfolio is, in general, not available. In this talk, I will start with a brief review of the different approaches to this problem that have been proposed in the literature and will show how the quadratic hedging scheme introduced, among others, by Föllmer, Schweizer, and Sondermann is applicable in this context under conditions that I will carefully spell out.
 

David Skovmand (Aarhus School of Business, University of Aarhus, Denmark)
Alternative Specifications for the Levy Libor Market Model: An Empirical Investigation (close abstract)

This paper introduces and analyzes specifications of the Levy Market Model originally proposed by Eberlein & Ozkan (2005). An investigation of the term structure of option implied moments shows that the Brownian motion and homogeneous Levy processes are not suitable as modelling devices, and consequently a variety of more appropriate models is proposed. Besides a diffusive component the models have jump structures with low or high frequency combined with constant or stochastic volatility. The models are subjected to an empirical analysis using a time series of data for Euribor caps. The results of the estimation show that pricing performances are improved when a high frequency jump component is incorporated. Specifically, excellent results are achieved with the 4 parameter Sato Variance Gamma model, which is able to fit an entire surface of caps with an average absolute percentage pricing error of less than 3%.
 

Jan Palczewski (Faculty of Mathematics, University of Warsaw, Poland)
Finite Horizon Optimal Stopping of Discontinuous Functionals with Applications to Impulse Control with Delay (close abstract)

Impulse control problems with finite time horizon, decision lag and execution delay lead naturally to optimal stopping of functionals with discontinuities with respect to the time-variable. I will discuss properties of the value functions of such stopping problems for continuous time Feller-Markov processes. I will demonstrate how to approximate the value function and the optimal stopping moment by solutions to discrete-time problems. I will show that in certain cases the optimal stopping problem can be reformulated in a more regular form which is better suited for existing PDE methods.
 

Michael Kupper, Nicolas Vogelpoth (Vienna Institute of Finance)
Seperation and duality in L0-modules (close abstract)

Many results in mathematical finance draw from Hahn-Banach's extension theorem and its consequences for hyperplane separation in locally convex vector spaces. However, in multi period discrete time or continuous time settings, the classical theorems from functional analysis are often not well suited and require a lot of work to apply. We will therefore generalize these classical theorems to L0-modules which we find more suitable to dynamic financial models. We first introduce a topology on L0 and we then introduce topologies on general L0-modules. Equipped with theses topological structures, L0-modules guarantee the existence of sufficiently many continuous linear forms in the sense that we can establish hyperplane separation theorems analogue to the classical theory. As a motivation of these concepts, we provide a module based approach to the Dalang-Morton-Willinger Fundamental Theorem of Asset Pricing in discrete time. In addition to this, we present a variety of L0-modules and we illustrate their applicability to selected problems in the theory of conditional risk measures. This includes, among others, Fenchel-Moreau type dual representations of conditional risk measures and their sub-differentiability.
 

Roman Ivanov (Lomonosov Moscow State University, Russia)
On calculation of multiple exercise Russian option (close abstract)

This work considers the problem of pricing of Russian (perpetual American lookback) option with rights to realize it for many times. The idea is to show possibility of creating a simple programmming procedure for calculation of the option's price and the set of optimal stopping moments in closed forms.
 

Jose Fajardo (IBMEC Business School, Rio de Janeiro)
Symmetry and Option Price Monotonicity with Levy processes (close abstract)

In this work we study the implications of the absence of symmetry, introduced in Fajardo and Mordecki (2006), and address the monotonicty with respect to the symmetry parameter and their applications.
 

Michael Schmutz (Institut f. math. Statistik und Versicherungslehre, Universität Bern)
Multivariate symmetry properties of asset prices, derivatives and their relation to convex geometry (close abstract)

It is possible to relate prices of several derivatives to certain convex bodies. This paves the way to relate many financial problems to the machinery of instruments provided by convex geometry. Furthermore, geometric properties can be translated into economic statements and vice versa. For instance, considering asset prices at maturity, the European put-call parity can be explained by point symmetry while the univariate duality-principle in option pricing corresponds to a reflection, explaining classical European put-call symmetry by line-symmetry. This motivates natural extensions of put-call symmetry in the multiasset setting. Interestingly, the well-known exchangeability of random vectors has a similar geometric interpretation and can be related to put-call symmetry with the help of a reduction of dimensionality by applying multivariate duality-principle techniques. In order to extend the range of applications, it is possible to transform some multivariate asymmetric distributions (bodies) to symmetric ones. A particular attention is devoted to the case of prices driven by Lévy processes. Both phenomena, multivariate put-call symmetry and exchangeability, can be applied for creating semi-static hedges of certain multiasset barrier options. If there is enough time, some other relations between financial questions and geometric phenomena will be discussed.
 

Peter Spreij (Universiteit van Amsterdam), Start-Seminar,
On Multivariate Feller conditions in term structure models (close abstract)

In the first part of the talk the relevance of the so-called Feller conditions in discrete time macro-finance term structure models is investigated. The Feller conditions are usually imposed on a continuous time multivariate square root process to ensure that the roots have nonnegative arguments, as shown in Duffie and Kan (1996). For a discrete time approximate model, the Feller conditions do not give this guarantee. Moreover, in a macro-finance context the restrictions imposed might be economically unappealing. At the same time, it has also been observed that even without the Feller conditions imposed, for a practically relevant term structure model, negative arguments rarely occur. Using models estimated on German data, we compare the yields implied by (approximate) analytic exponentially affine expressions to those obtained through Monte Carlo simulations of very high numbers of sample paths. It turns out that the differences are rarely statistically significant, whether the Feller conditions are imposed or not. Moreover, economically the differences are negligible, as they are always below one basis point. We conclude by observing that a model with a single volatility factor for which the Feller conditions are violated is already adequate.

In the second part we turn back to continuous time models. We will prove its necessity for a 2-dimensional square root system of SDEs in two cases. In the first case there are two linearly independent volatility processes and in the second case there is only one and the same volatility process in the diffusion parts of the two SDEs. In fact we present a procedure to construct models that exhibit negative volatilities (properly defined). The approach is based on measure transformations and solving linear systems of ordinary differential equations. The underlying simple idea is that a random variable is negative with positive probability if it has negative expectation. We construct a probability measure under which we can apply this idea.

(joint work with Enno Veerman and Peter Vlaar)

Johannes Leitner (Finanz- und Versicherungsmathematik, TU Wien)
12:00, FH Hörsaal 3
Habilitation Talk: Robust Martingale Representations for Marked Point Processes (close abstract)

We develop a super-additive (insurance) market model based on marked point processes. A dynamic premium calculation principle is used for pricing of instantaneous insurance contracts. Completeness and absence of arbitrage is shown for the market model and can be interpreted as a 'robust' predictable uniformly bounded martingale representation property of the random measure corresponding to the marked point process.
 

Philip Dybvig (Olin School of Business, Washington University, Saint Louis, USA)
16:30, SEM 107
High Hopes and Disappointments: Preference for Timing of Information without the Recursive Structure (close abstract)

Recursive Utility models generalize von Neumann-Morgenstern preferences by giving agents preference over the timing of resolution of uncertainty. These preferences have been given an axiomatic foundation by Kreps and Porteus [1978, 1979] and additional theoretical and empirical development by L. Seldon [1978], Epstein and Zin [1989, 1991], and others. We provide a generalization of these models which does not have the recursive structure. In recursive models, preferences looking forward do not depend on past consumption or beliefs. In our model, preferences looking forward also do not depend on past consumption, but they can depend on past beliefs, or perhaps more generally and more accurately on what was expected to happen on other branches of the tree. Preferences in our model are not defined recursively, which avoids the questions of existence that can be difficult in settings with continuousr time and/or an infinite horizon. We use our new model of preferences to derive optimal consumption and investment strategies, which can still be solved using dynamic programming but with an extra state variable.
 

Goncalo dos Reis (HU Berlin)
Differentiability of quadratic growth BSDEs and applications (close abstract)

We present results concerning classic and variational differentiability for quadratic growth BSDEs. We browse through the main tools used in the proofs and show several implications of the differentiability results, namely applications to crosshedging of derivatives, path regularity results for the control variable and numerical schemes.

PRisMa 2008
One-Day Workshop on Portfolio Risk Management
(FH HS 8 - Nöbauer Hörsaal, "Freihaus" Building of TU Wien)

Simone Farinelli (UBS, Zürich)
13:30, SEM 107

Geometric Arbitrage Theory (close abstract)

On the theoretical side: a differential geometric framework is introduced to translate any market model into a principal fibre bundle allowing to interpret arbitrage as curvature, parameterizing arbitrage opportunities with the Lie Algebra of the holonomy group. The no arbitrage condition is equivalent to a continuity equation and the total market arbitrage can be defined by as an integral over the market of the continuity expression. The market total arbitrage is computed is some special cases.

On the practical side: a methodology to simulate the future evolution of asset values is proposed with following characteristics
- the dimension of risk factors can be reduced.
- the no arbitrage condition is satisfied.
- the simulated moments of asset returns match the empirical ones.
 

Olaf Menkens (School of Mathematical Sciences, Dublin City University)
10:30, SEM 107

Crash Hedging Strategies and q-Quantile Crash Hedging Strategies (close abstract)

The worst–case scenario portfolio problem which has been introduced by Korn and Wilmott (2002) will be considered in this presentation. Although they assume that the probability of a potential jump occurring is unknown, this talk analyses how the worst–case scenario portfolio problem is affected if the probability of a crash arising is known.
The result is that the additional information of the known probability is not used in the worst–case scenario. This leads to a q–quantile approach (instead of a worst–case), which can be considered as a Value at Risk approach with respect to the potential jump in the optimal portfolio problem.

 

Denis Belomestny (Weierstrass Institute for Applied Analysis and Stochastics, Berlin)
New series representations for the characteristic functions of affine Feller processes with applications to option pricing (close abstract)

In a rather general setting of Itô-Lévy processes we study a class of conditional transforms of a process which are holomorphic in some disc around time zero in the complex plane. In particular, we will show that for affine Itô-Lévy processes the Fourier transform is holomorphic in a time strip under some stationarity and moment conditions. Finally, explicit series representations for multidimensional affine processes with state dependent jump part will be given and some applications to option pricing in such models will be discussed.
 

Mark Freidlin (University of Maryland), Start-Seminar,
Asymptotic Problems for PDE's and Related Stochastic Processes (close abstract)

Behavior of solutions of boundary problems for second order elliptic or parabolic PDE's under small, in one or another sense, perturbations of the operator is an important question for the theory of differential equations.
A diffusion process corresponds to each elliptic, maybe degenerate, operator, and the behavior of solutions is closely related to the behavior of corresponding processes. In the same time, the processes can be investigated by pure probabilistic methods such as stochastic differential equations, limit theorems for stochastic processes. Exactly in this way, main results on the limiting behavior of solutions of PDE's with a small parameter in higher derivatives were obtained. Later some of those results were re-proved by analytic methods.
I will speak on two new classes of such kind of problems. The averaging principle and large deviation theorems for solutions of stochastic differential equations are the main tools in this study.
 

Matthias Weber (University of Applied Sciences, Dresden)
On Stochasticity of Solutions of Differential Equations with a Small Delay (close abstract)

The first part of the talk will give a short overview of joint results with Mark Freidlin on asymptotic problems for dynamical systems and diffusion processes with small parameters.
In the second part, I will show how these results can be applied to the study of a class of differential equations with a small delay. The solutions of such equations can be approximated, in a sense, by a stochastic process on a graph associated with the equation. This process moves as a deterministic motion inside any edge of the graph, but, after reaching an interior vertex of the graph, the process chooses one of the other adjacent edges to proceed there with a certain probability. These probabilities are calculated explicitly. The stochasticity is an intrinsic property of the differential equation with small delay. This is also joint work with Mark Freidlin.
 

Pavel Shevchenko (CSIRO, Sydney)
16:30, FH 2
Model risk in claims reserving within Tweedie's compound Poisson models (Slides),
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Angelika May (Universität Oldenburg)
CPPI Models for life insurance products with guarantees CANCELLED! (close abstract)

Unfortunately Prof. May had to cancel the talk due to health reasons.

We discuss and compare different approaches for unit linked life insurance products with guarantee, with focus on hybrid products on the one hand, and CPPI products on the other hand. We will show some simulation results for a simple model and then continue with a theoretical view on models with jumps.
 

Andrea Freiberger (TU Wien), Start-Seminar,
Distribution properties of digital (0,1)-sequences (close abstract)

In the first part of this talk a short overview of sequences used in Quasi Monte Carlo theory together with some examples of their application to financial mathematics will be given. Further the quality of their results will be compared to the quality of results coming from Monte Carlo Methods. The second part will deal with low discrepancy sequences in dimension one. Some bounds for the discrepancy of special sequences will be given along with some results for their asymptotic behavior.
 

Harald Oberhauser (University of Cambridge, UK)
Isoperimetry and Rough path regularity (close abstract)

The first part of the talk will be a short, informal overview of rough path theory. The second part will be a discussion on how to establish optimal regularity and integrability results for variation norms of Gaussian processes taking values in a metric space (especially Gaussian rough paths). On our way we will encounter classic theorems from the theory of stochastic processes like Taylor's optimal variation result, Fernique's theorem and the isoperimetric inequality on Wiener space. No previous knowledge of the above is needed and I'll try to give good motivation for all these topics.
 

Umut Cetin (London School of Economics, United Kingdom), Start-Seminar,
Insider trading in credit markets with dynamic information asymmetry (close abstract)

We study an equilibrium model for a defaultable bond in the setting of Back-Pedersen. The market consists of noise traders, an insider and a risk-neutral market maker. Under the assumption that the insider observes the firm value continuously in time we study the optimal strategies for the insider and the optimal pricing rules for the market maker. We show that there exists an equilibrium where the insider's trades are inconspicuous. In this equilibrium the insider drives the total demand to a certain level at the default time. The solution follows from answering the following purely mathematical question which is of interest in its own:
Suppose Z and B are two independent Brownian motions with B(0)=0 and Z(0) is a positive random variable.
Let T be the first time that Z hits 0. Does there exists a semimartingale X such that
1) it is a solution to the SDE dX_t=dB_t + g(t,X_t, Z_t)dt with X(0)=1 , for some appropriate function g,
2) T is the first hitting time of 0 for X, and
3) X is a Brownian motion in its own filtration?
 

Corina Constantinescu (RICAM Linz)
Risk procesess with stochastic returns on investments (close abstract)

In this talk a literature survey on different methods for the analysis of risk processes with stochastic returns on investments will be given. Starting from general investigations on random difference equations we deal with discrete and continuous time models in collective risk theory with both light and heavy tailed claim size distributions. A particular emphasis will be given to pointing out differences of methodologies to address asymptotic issues in this context.
 

Elisa Nicolato (University of Aarhus)
Sato Processes in Default Modelling (close abstract)

Classically, in reduced form default models the instantaneous default intensity is the modelling object and survival probabilities are given by the Laplace transform of cumulative hazard process, its integral. Instead, recent literature has shown a tendency towards specifying the cumulative hazard process directly. We present a new framework where survival probabilities are still obtained in closed form but where the cumulative hazard process belongs to the class of self-similar additive processes also termed Sato processes. We analyze two specifications for the cumulative hazard process; Sato-Gamma and Sato-IG processes corresponding to the Gamma law and Inverse Gaussian law respectively. The models are calibrated to data on the single names included in the iTraxx Europe index and compared with two Ornstein-Uhlenbeck type intensity models. It is shown how the Sato models achieve similar calibration errors with fever parameters, and with more stable parameter estimates in time. (Joint work with Thomas Kokholm.)
 

Erik Baurdoux (LSE London), Start-Seminar,
The McKean stochastic game driven by a spectrally negative Lévy process. (close abstract)

The McKean stochastic game (MSG) is a two-player version of the perpetual American put option. The MSG consists of two agents and a certain payoff function of an underlying stochastic process. One agent (the seller) is looking for a strategy (stopping time) which minimises the expected pay-off, while the other agent (the buyer) tries to maximise this quantity.
For Brownian motion one can find the value of the MSG and the optimal stopping times by solving a free boundary value problem. For a Lévy process with jumps the corresponding free boundary problem is more difficult to solve directly and instead we use fluctuation theory to find the solution of the MSG driven by a Lévy process with no positive jumps. One interesting aspect is that the optimal strategy for the minimiser "thickens" from a point to an interval in the presence of jumps.
This talk is based on joint work with Andreas Kyprianou (University of Bath).
 

Semyon Malamud (ETH Zürich)
14:00, SEM 138A
Equilibrium Asset Prices (close abstract)

In this talk we will discuss the behavior of equilibrium asset prices in heterogeneous exchange economies. We will start with complete market economies and study the long run asymptotic behavior of asset prices and the horizon goes to infinity. As it turns out, there is a whole family of dominant agents, one for each asset type, dominating the long run prices.
In the second part of the talk, we will discuss equilibria in incomplete markets. Because of extreme non-linearity of the equation, incomplete market equilibria are very difficult to analyze. We will discuss new methods and techniques for controlling them. The talk is partly based on a joint work with Eugene Trubowitz.
 

Achim Wübker (Universität Göttingen)
L2-Spectral gaps for Markov-chains (close abstract)

We analyze the spectral properties of Markov operators induced by Markov chains with general state space on certain L2-spaces. Especially we are interested in the question, whether the associated Markov-operator has the spectral gap property or not. For this we work out three approaches: The first one is based on a work of Lawler & Sokal. We extend this by defining a family of constants in order to obtain necessary and sufficient conditions for the existence of an L2-spectral gap. These conditions are simplified in the case of reversible and weak reversible chains. The second approach uses entropy, especially some growth of entropy associated to the Markov-operator. Defining two different growth conditions, we get again necessary and sufficient conditions for the existence of L2-spectral gaps. Finally we investigate the connections between a.s. geometric ergodicity and the spectral gap property and obtain some new results for the non-reversible case. Additionally we get a new global limit theorem for a sequence of random variables induced by Markov chains for the case of non-normal, \alpha stable limit distribution.

Mladen Savov (University of Manchester), Start-Seminar,
Small Time Behaviour of Lévy Processes: Laws of the Iterated Logarithm (close abstract)

The Law of the Iterated Logarithm (LIL) is one of the deepest results in the classical theory of probability. Historically, any stochastic process whose maximal rate of growth is described a deterministic function is said to exhibit LIL behaviour.
In this talk some new results on the small time behaviour of Levy processes will be presented. A comparatively systematic way of describing the deterministic functions, such that scaled with them, the rate of growth of the absolute maximum and the maximum of a Levy process is 1. It is shown that there cannot be a universal link between the characteristics of the Levy process and these functions. Integral criteria will be introduced for checking whether a given function describes the maximal rate of growth for any Levy process with unbounded variation.

Christian Bayer
Harmonic analysis of stochastic equations and backward stochastic differential equations (close abstract)

I present parts of the aforementioned paper of Freddy Delbaen and Shanjian Tang, in which very general existence and uniqueness theorems for (backward) stochastic differential equations are proved. The authors heavily use martingale duality theory, and obtain very precise statements in terms of integrability results for the solutions.

Anders Szepessy (Stockholm University), Start-Seminar,
Langevin molecular dynamics derived from Ehrenfest dynamics (close abstract)

One ab initio method to simulate molecular dynamics is to use Ehrenfest dynamics, also called quantum classical molecular dynamics, where classical nuclei are coupled to quantum modeled electrons. In this talk I will derive stochastic Langevin molecular dynamics for the nuclei from Ehrenfest dynamics, at positive temperature, assuming that the molecular bulk system is in equilibrium and that the initial data for the electrons is stochastically perturbed from the ground state.

Pierre Moussa (CEA/Saclay, Gif sur Yvette, France), Start-Seminar,
On the representation of Tr exp(A-tB) as a Laplace transform (close abstract)

An old conjecture made in 1975 by Bessis, Villani and myself occured in trying to prove exact results in quantum statistical mechanics. The conjecture states that $Tr(\exp (A-tB))$ is the Laplace transform in the variable $t$ of a positive measure when A and B are semi definite hermitian operators. Still unresolved for dimension greater than two, the question received for the finite dimensional case, a new formulation by Lieb and Seiringer in 2004. In this new version, it is asserted that if A and B are semidefinite matrices, the coefficients of $t^r$ in $Tr((A+tB)^p)$ are all non negative. This more algebraic version of the conjecture produced a renewal of interest for the conjecture, which is now considered under several different point of views. We will present both the historical and the most recent aspects of the question.

Josef Teichmann, Start-Seminar,
How to calculate moments of affine processes easily (close abstract)

We show an invariance property of affine processes and related classes. We show how to calculate by means of this property arbitrary moments of the respective processes precisely and how to apply those results to some questions of pricing and hedging.

Paul F.X. Müller (JKU Linz)
Compensated Compactnes, Separately convex Functions, and Interpolatory Estimates between Riesz Transforms and Haar Projections (close abstract)

We discuss a problem by L. Tartar on semi-continuity of separatly convex integrands and its recent solution, obtained in collaboration with J. Lee and S. Müller. New interpolatory estimates between the directional Haar projections and Riesz transforms form the analytic backbone of our approach. (Preprint available at http://shrimp.bayou.uni-linz.ac.at/Papers/publ-mueller.html).

Diana Auerswald (University of Oldenburg)
Valuation of American Style Options - Extension and Empirical Tests of a Nonparametric Pricing Algorithm (close abstract)

A nonparametric method of pricing American style options based solely on historical asset price data was recently developed by Alcock and Carmichael [2008] (AC08). The method is the nexus of the canonical valuation approach introduced by Stutzer [1996] for European-style options and the least-squares Monte-Carlo algorithm of Longstaff and Schwartz [2001]. Alcock and Auerswald [2008] derive an extension to this method to include conditioning information from a small number of observed option prices. This additional information improves the overall accuracy of the method and enables pricing of illiquid options in an incomplete market. Using a series of simulation studies and an empirical study the statistical properties and the applicability of both AC08 and the extension are explored. The empirical study uses a large sample of OEX American options traded on the S&P 100 index. In both the simulation study and the empirical study AC08 slightly outperforms a traditional Black-Scholes estimator and a numerical estimator (Crank-Nicholson) using historical volatility. In contrast, the extension to AC08 produces significant reductions in mean pricing errors and performs comparably well to implied-volatility Black-Scholes pricing, in particular for out-of-the-money American put options. In the empirical study the historical volatility Black-Scholes and Crank-Nicolson valuation and AC08 clearly underperform both the extension of AC08 and the implied volatility Black-Scholes model. The results of the simulation and the empirical studies encourage the application of the nonparametric approaches to price American options. This is particularly true for more frequently traded options.

Yuri Kifer (Hebrew University, Jerusalem)
11:30, Sem 107
Game options, shortfall risk and their binomial approximations (close abstract)

Game (Israeli) options which I introduced in 2000 extend the setup of American options by allowing their issuer to call them back (cancell) paying certain penalty for that. Pricing of such options leads to Dynkin's optimal stopping games. In a series of papers, partially with Y. Dolinsky, we studied error estimates for binomial approximations of prices, shortfall risks and corresponding hedging strategies for usual and barrier type game options which provide via dynamical programming recurrent formulas an effective way of their computations. Similar and sometimes stronger results follow for American options even in a simpler way yet providing new results even in this heavily studied case. The methods rely on the Skorokhod embedding of sums of i.i.d. random variables into the Brownian motion and on the risk representation via the dynamical programming scheme in the discrete time case while the barrier options require also to take care about discontinuities of the payoffs. In the multidimensional case where Skorokhod'd embedding does not work we should employ other strong approximation methods.

Roman Muraviev (Tel-Aviv University)
Growth Gap vs. Smoothness for Diffeomorphisms of The Interval (close abstract)

Given a diffeomorphism of the interval, consider the uniform norm of the derivative of its n-th iteration. We get a sequence of real numbers called the growth sequence. Its asymptotic behavior is an invariant which naturally appears both in smooth dynamics and in geometry of the diffeomorphisms groups. We find sharp estimates for the growth sequence of a given diffeomorphism in terms of the modulus of continuity of its derivative. These estimates extend previous results of Polterovich and Sodin, and Borichev. (Joint work with L. Buhovsky)

Ales Cerny (Cass Business School, City University London)
Mean-Variance Hedging and Optimal Investment in Heston's Model with Correlation (close abstract)

In this talk we use recent results on mean-variance hedging for general semimartingale processes to solve the mean-variance hedging problem in Heston's model with a stochastic opportunity set moving systematically with the volatility of stock returns. We allow for correlation between stock returns and their volatility (so-called leverage effect).
Our contribution is fourfold: using a new concept of opportunity-neutral measure we present a simplified strategy for computing a candidate solution in the correlated case. We then go on to show that this candidate generates the true variance-optimal martingale measure; this step seems to be partially missing in the literature. We derive formulas for the optimal hedging strategy and the hedging error. Finally, we reformulate the mean-variance hedging problem to obtain Sharpe ratio price bounds for any square-integrable contingent claim.
(This is joint work with Jan Kallsen, CAU Kiel).

Sergei Kucherenko (Imperial College London)
Application of Global Sensitivity Analysis and Quasi Monte Methods in finance (close abstract)

Monte Carlo simulation is an important tool in the pricing of complex path dependent financial instruments and in risk management. The convergence rate of MC methods is O(1/sqrt(N)), where N is the number of sampled points or simulated paths. It does not depend on the number of dimensions (variables) d although it is rather slow. A higher rate of convergence can be obtained by using deterministic uniformly distributed sequences called low-discrepancy sequences (LDS) instead of pseudo-random numbers. Methods based on the usage of LDS are known as Quasi Monte Carlo (QMC). Asymptotically, QMC can provide a rate of convergence O(1/N). Modern financial instruments are very high dimensional. Situation is far from clear at high dimensions, where general theory predicts deterioration of QMC efficiency. We applied Global Sensitivity Analysis (GSA) to explain the success of QMC methods in finance. GSA enables the identification of key parameters whose uncertainty most affects the output. It can be used to rank variables, fix unessential variables or decrease problem dimensionality. As a model problem two well-known approximations of Wiener path integral were considered: the standard and the Brownian bridge discretizations. It is shown that the much faster convergence rate of the Brownian bridge algorithm is caused by the change of a number of important variables (or reduction of the effective dimension). We also present some other results and schemes showing the superiority of QMC over MC methods in finance.

Claudia Czado (TU München, Germany)
Pair-copula constructions of multiple dependence (close abstract)

In this talk we introduce pair-copula constructions (PCC) for flexible multivariate copulas (see Aas et al (2007)). As pair copulas for example one can utilize bivariate Gaussian copulas, t-copulas, Clayton or Gumbel copulas. The specific PCC and its parameters can be estimated using maximum likelihood. However confidence intervals are difficult to construct. Therefore we follow a Bayesian approach. Model selection among different PCC's are facilitated using reversible jump MCMC introduced by P. J.Green (1995). For comparing few models an approach suggested by P. Congdon (2006) using separate MCMC runs to estimate Bayes factors can be used alternatively. The proposed models and inference algorithms are applied to financial return data demonstrating the usefulness of PCC's. This is joint work with A. Min.

(Slides)

Nicolas Bouleau (École Nationale des Ponts et Chaussées), Start-Seminar,
On Dirichlet forms generated by the arbitrary functions principle (close abstract)

When a random variable is approximated by another, the asymptotic error yields a Dirichlet form. This is a general result valid in finite or infinite dimensional frameworks. Usually the squared field operator is given asymptotically by the conditional variance of the error. There are nevertheless cases where the approximate random variable is a deterministic function of the limit, but where the Dirichlet form doesn't vanish. This phenomenon is interesting in the sense that a deterministic device yields a stochastic result if we think a Dirichlet form as an expression of a second order operator.
The arbitrary functions principle (willkürliche funktionen) is an example of such a situation. Studied by Poincaré and then by Hopf, it gives a mathematical argument of the fairness of the roulette or of a lottery wheel. We generalize some of these ideas to the Wiener space, and obtain consequences on some stochastic differential equations.

Andrey Selivanov
Pricing of Contingent Claims based on Tail VaR (close abstract)

The No Arbitrage pricing technique gives us very wide interval of fair prices. There were proposed many approaches that narrow this interval. One of them is the so-called No Good Deals pricing technique based on coherent risk measures. Let us say that a number is a fair price for a claim if the introduction of this claim with this price doesn't produce any trade with negative risk. We find the upper price and a superhedging strategy for a static model, where the set of attainable incomes has a unique risk-neutral measure. We suppose that the risk is measured via Tail VaR.

Nicolas Bouleau (École Nationale des Ponts et Chaussées)
18:00, FH 2
What are the philosophical probabilities? (close abstract)

(Quand le hasard fait bien les choses)

put the mouse on the diagram
 

In the middle of the 19th Century, the philosopher and economist Augustin Cournot thought about what makes that we believe that some data are not random but governed by a rule. His opinion is that this belief is not quantifiable and is a matter for philosophical probabilities in opposition to mathematical probabilities.
Following this idea, we propose a walk through the conflicts between chance and sense.
The question was put already by the Ancients and brilliantly by Cicero (De divinatione) who, being himself augur, didn't believe to divination. More recently it became a challenge at the birth of the abstract art and of the modern architecture insofar as it was said: what nonsense! It has been a trap fot the famous linguist Ferdinand de Saussure and threw him in an anxious perplexity. It is then in the heart of the debate in biology around the book of Jacques Monod  Le hasard et la nécessité and it enlightens the critics of some  scientists on the idea of "roulette" of the life or of the evolution. It has been transformed into a method by Freud in psychoanalysis. Now, it is also fundamental in our propensity to believe the scientific representations and there is the main issue  of this reflexion.

Further reading material (PDF in German/French).

Ilya Pavlyukevich (Humboldt-Universität, Berlin), Start-Seminar,
Exit times of small-noise Lévy-driven diffusions (close abstract)

We study the first exit times of solutions of small noise Levy-driven diffusions from an interval in dependence on the weight of the tails of the jump measure. In particular, we consider power, sub- and super-exponential tails, and compare the results with the well-known Gaussian case. (Joint work with P. Imkeller and T. Wetzel, HU Berlin)

Michel Emery (Université Louis Pasteur, Strasbourg)
On one-dimensional Brownian motions immersed in a two-dimensional one (close abstract)

Brownian motion is the most fundamental and most familiar stochastic process, but its filtration is still far from having revealed all its secrets. For example, recognizing when a given filtration is generated by some BM is often a difficult problem. The talk will focus on questions which arise naturally when one considers one-dimensional BMs in the filtration generated by some 2-dimensional BM. (Joint work with J. Brossard and C. Leuridan.)

Miklos Rasonyi
16:15, SEM 104
Hidden Markov Processes
Vortragsreihe: Wissenswertes der Mathematik, details

Mykhaylo Shkolnikov (Stanford University), Start-Seminar,
Affine matrix-valued diffusions

Paul Embrechts (ETH Zurich)
19:00, math-space, Museumsplatz 1 (Ovaltrakt e-5.4), 1070 Wien
Holländische Deiche und Risikokapital für Banken und Versicherungen (close abstract)

Wie geht man mit Risiken um, rational und effektiv? Wann wird ein Risiko als tolerierbar eingestuft? Die klassische Antwort lautet: Wenn die Kosten für seine Minimierung höher sind als die Kosten, die man bei Eintritt des Risikos zu erwarten hat. Nicht allein die Flutkatastrophe des Jahres 1953 in Holland, auch Risiken bei Hedgefonds und die jüngsten Kreditausfälle im US-Immobilienmarkt, die sogar zur Existenzkrise von europäischen, im nationalen Geschäft verwurzelten Instituten führten, kommen bei diesem math.space-Vortrag zur Sprache.

Paul Embrechts (ETH Zurich)
18:15, Festsaal der ÖAW, Dr. Ignaz Seipel-Platz 2, 1010 Wien
Quantitative Risk Management,
Johann Radon Lectures (close abstract)

Über Mathematik und Risiko bei Banken und Versicherungen: Auch in der Welt der Banken und Versicherungen findet sich eine Vielzahl von Beispielen für den heutigen Drang nach Akronymen. Relevant für diesen Vortrag sind die folgenden: QRM (Quantitative Risk Management), ERM (Enterprise Risk Management), GRM (Global Risk Management).
QRM befasst sich mit der Fragestellung der quantitativen Analyse von Risiken. Aufsichtsrechtliche Gremien sind ein starker Antrieb für Banken und Versicherungen diese Quantifizierung voran zu treiben. Auf Basis dieser Analyse wird Risikokapital berechnet um mit hoher Wahrscheinlichkeit unerwartete Marktereignisse abfangen zu können.
Im Vortrag werden folgende Themen aus dem Bereich des QRM herausgegriffen: Value-at-Risk, Extremalereignisse, Abhängigkeitsmodellierung, Risikoaggregation, Operationelles Risiko. Eine entscheidende Frage für die Praxis ist die Differenzierung zwischen Finanzrisiken, die sich sinnvoll quantitativ erfassen lassen und solchen, bei denen ausschließlich eine qualitative Beschreibung Sinn macht. Neben der quantitativen Messung von Risikozahlen ist auch ihre Aggregation eine wichtige Aufgabe des QRM, deren Lösung anspruchsvolle Mathematik erfordert.
Die fundamentale Rolle der Mathematik in den Bereichen der Preisbestimmung und Absicherung von Finanzderivaten (Optionen, Kreditderivate, Swops...) ist unbestritten. Die Hauptthese ist, dass auch bei regulatorischen Fragestellungen aus den Bereichen der Finanz- und Versicherungsaufsicht die Mathematik nicht weg zu denken ist. Anhand mehrerer Beispiele wird versucht diese These zu belegen. Ein wichtiges Korollar ist die Tatsache, dass die Bedeutung von gut ausgebildeten Studenten aus der angewandten Mathematik für die Wirtschaft groß bleiben wird. Schlussendlich bieten Fragestellungen des QRM eine Fülle von äußerst interessanten und anspruchsvollen Forschungsproblemen.

Sühan Altay (Middle East Technical University, Istanbul)
On forward interest rates: via random fields and nuclear space valued semi-martingales (close abstract)

The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, firstly the drift condition of the forward rate dynamics, in which they are governed by two-parameter processes, is given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country interest rate model, term structure of defaultable bond prices and forward measures. Finally, a general framework for bond prices via nuclear space valued semi-martingales is introduced. In that model, stochastic components of the forward rate dynamics are taken to be stochastic integrals on a pair of nuclear spaces in duality. We also give the drift condition for the Levy random field case as an example to the proposed model.

Christian Bayer, Josef Teichmann, Richard Warnung, Start-Seminar,
Implementation of new hypo-elliptic simulated annealing algorithms (close abstract)

We demonstrate implementations of some new recently found simulated annealing algorithms, where less Brownian motions than space dimension are applied, in dimension 3 and 5. Several numerical and theoretical aspects are discussed.

Christina Ziehaus
10:15, Sem 107
Optimal Consumption and Terminal Wealth (close abstract)

Starting from a classic market model we compare the primal and the dual approach for the solution of the optimal consumption and terminal wealth problem. We will also give an outlook on the application of the dual method on an OU-market.

Eugen Puschkarski (Treasury Division, ÖNB)
18:00-20:30, Zeichensaal 3 (Freihaus, 7th floor, green section)
Ex post risk attribution in a value-at-risk framework
Austrian chapter meeting of Global Association of Risk Professionals (GARP)

Ansgar Jüngel (TU Vienna), Start-Seminar,
Entropy and entropy dissipation in nonlinear diffusion equations (close abstract)

Many dynamical problems in applications give rise to a Lyapunov functional which is nonincreasing in time. If diffusion or dissipation is involved, this leads to functional inequalities which often allow to conclude convergence of the solutions to equilibrium. Since the physical entropy is usually a special case of such functionals, we call these inequalities entropy-entropy dissipation inequalities. In recent years, they have been much studied since they allow for a deep understanding of the dynamics of the solutions of the partial differential equations. Moreover, there are surprising connections to mass transportation theory and probability theory. A wide range of diffusion equations can be treated, for instance cross-diffusion systems and higher-order equations like the thin-film equation. In this talk it will be explained how entropy-entropy dissipation techniques may be used in the existence analysis, the study of the long-time behavior of the solutions, and for the derivation of new inequalities of logarithmic Sobolev type. Furthermore, a new method of deriving entropy inequalities in an algorithmic way will be introduced. The idea is to reformulate the integration by parts as a decision problem for polynomial systems (well-known in real algebraic geometry) which can be solved in principle by computer algebra systems.

Bertram Düring (TU Vienna)
An inverse problem in option pricing and kinetic models for wealth distribution (close abstract)

Numerical Methods for optimal control of systems described by partial differential equations (PDE) have been studied widely and successfully applied to many problems. In the first part of this talk we consider the problem of identifying local volatility functions from market option prices. Mathematically the problem can be formulated as a PDE constrained optimal control problem. We propose an algorithm that is based on sequential quadratic programming and on a primal–dual active set strategy that guarantees pointwise bilateral constraints for the volatility. We present analytical and numerical results.
In the second part of the talk, we consider kinetic agent models for wealth distribution in simple economies. Based on "microscopic" interactions these models develop "macroscopic" features in the long-term limit like stationary wealth distributions with Pareto tails that are observed also in empirical data. We report some recent analytical and numerical results on the speed of relaxation towards the stationary state.

Florian Leisch, Start-Seminar,
Stochastic Portfolio Theory - How do functionally generated portfolios perform under real market conditions? (close abstract)

Following known models in stochastic portfolio theory we present some approaches to building equity portfolios by means of generating functions. With these methods we simulate portfolios in the MSCI EMU universe. Based on the obtained results, we compare the effectiveness of these techniques.

Richard Warnung
On the construction of an integrand hiding the drift of a Brownian motion with drift (close abstract)

We consider the construction of a Brownian motion with a tailor-made but non-trivial drift S such that we can find an integrand H fulfilling that the stochastic integral H ⋅ S is a Brownian motion (without drift) in its own filtration - this is the filtration generated by H ⋅ S. (This is joint work by Miklós Rásony, Walter Schachermayer, and Richard Warnung.)

Josef Teichmann, Start-Seminar,
Cubature on Wiener Space in infinite dimensions (close abstract)

We prove a stochastic Taylor expansion for SPDEs and apply this result to obtain cubature methods, i.e. high order weak approximation schemes for SPDEs, in the spirit of T. Lyons and N. Victoir. We can prove a high-order weak convergence for well-defined classes of test functions if the process starts at sufficiently regular points. We can also derive analogous results in the presence of Lévy processes of finite type, here the results seem to be new in finite dimension. Several numerical examples are added.

Axel Helmert (FJA)
16:30, FH 2
Finanzmathematische und Aktuarielle Methoden im Wandel: Die Internationalisierung der Märkte in der Lebensversicherung und Altersvorsorge und ihre Auswirkung auf die mathematische Praxis,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Christina Niethammer (Universität Konstanz), Start-Seminar,
Portfolio Optimization and Optimal Martingale Measures in the Presence of Unbounded Jumps (close abstract)

We discuss the relation between utility maximization problems with respect to isoelastic type, -|1-ax/p|^p, and exponential utility functions, -exp(-ax), a>0. Optimal terminal values as well as their optimal portfolios are obtained from convex duality mainly for exponential Lévy processes. Convergence of the portfolios is proved thanks to the convergence of the dual solutions, i.e. the convergence of q-optimal (signed) martingale measures, qSMM, to the minimal entropy one, MEMM. [JKM] prove this convergence of the measures but within the class of equivalent martingale measures only and under conditions which typically fail under unbounded upward-jumps. In the presence of (unbounded) jumps, however, q-optimal signed martingale measures may fail to be equivalent. We present a verification procedure based on the dynamic portfolio optimization problem yielding an explicit representation of qSMM. While significantly relaxing conditions in [JKM], we discuss when qSMM is equivalent. In contrast to [JKM] our conditions include typical models as the Kou, Merton, or Variance-Gamma model. Finally, we establish convergence of qSMM to MEMM under an integrability condition.
[JKM] Jeanblanc, M., Klöppel, S., and Miyahara, Y. (2007), Minimal F^Q-Martingale Measures For Exponential Lévy Processes, Ann. Appl. Probab., 17, 5/6, 16151638.

Claudia Ravanelli (Swiss Banking Institute, Zurich)
Cash Sub-additive Risk Measures and Interest Rate Ambiguity (close abstract)

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub additive axiom to preserve the original difference between the numeraire of the current reserve amounts and future positions. Consequently, cash sub-additive risk measures can model stochastic and/or ambiguous interest rates or defaultable contingent claims. Practical examples are presented and in such contexts cash additive risk measures cannot be used. Several representations of the cash sub-additive risk measures are provided. The new risk measures are characterized by penalty functions defined on a set of sub-linear probability measures and can be represented using penalty functions associated with cash additive risk measures defined on some extended spaces. The issue of the optimal risk transfer is studied in the new framework using inf-convolution techniques. Examples of dynamic cash sub-additive risk measures are provided via BSDEs where the generator can locally depend on the level of the cash sub-additive risk measure. (Joint work with Nicole El Karoui)

One-day mini-workshop on Calibration, Levy processes in finance, FFT, and related issues
(Freihaus Building of TU Wien)

Stefan Tappe (Vienna Institute of Finance), Start-Seminar,
Invariant submanifolds for Levy driven stochastic equations (close abstract)

We deal with finite dimensional invariant submanifolds for Levy driven stochastic equations. Due to the jumps of the Levy process, the geometric situation becomes more delicate than in the continuous Wiener driven case. Our investigations lead to the study of foliations of linear submanifolds, which includes linear submanifolds in particular. In both cases, a characterization of the invariance problem is achieved and we show how to compute the corresponding coordinate process, provided local invariance prevails.

Walter Schachermayer
In which Financial Markets do Mutual Fund Theorems hold true? (close abstract)

The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. It is established that:
(i) Let N be the wealth process of the numéraire portfolio (i.e. the optimal portfolio for the log utility). If any path-independent option with maturity T written on the numéraire portfolio can be replicated by trading only in N, then the (MFT) holds true for general utility functions, and the numéraire portfolio may serve as mutual fund. This generalizes Merton’s classical result on Black-Scholes markets. Conversely, under a supplementary weak completeness assumption, we show that the validity of the (MFT) for general utility functions implies the same replicability property for options on the numéraire portfolio described above.
(ii) If for a given class of utility functions (i.e. investors) the (MFT) holds true in all complete Brownian financial markets S, then all investors use the same utility function U (modulo affine transformations), where U must be of HARA type. This is a negative result in the spirit of the classical work by Cass and Stiglitz.

Antonis Papapantoleon, Start-Seminar,
The duality principle for multidimensional semimartingales (close abstract)

The duality principle in option pricing states that the price of a call option on an asset S=e^H under a meaure P is equal to the price of a put option on an asset S'=e^H' under a suitable dual measure P'. Applications to several exotic options are also possible. In this talk we aim to explore the extension of this statement to markets with several assets. We consider assets driven by general semimartingales, construct dual measures and determine the triplet of predictable characteristics of the dual process under these measures. Several ways to prove these results are shown. As applications, we can relate the price of swap and quanto options to standard call options. More explicit computations are presented for Lévy process and general diffusions.

Gabriel Maresch
Optimality and Monotonicity in the Monge-Kantorovich Optimal Transportation Problem (close abstract)

It is known that for cost functions which are either lower semi-continuous and finite or continuous and possibly infinite, transport plans which are concentrated on a c-cyclically monotone set are automatically optimal. We present related results which hold in a more general context, namely for Borel measurable cost functions. Concepts similar to c-cyclically monotonicity such as robust optimality and strong c-monotonicity are explored further. (Joint work with M. Beiglboeck, M. Goldstern and W. Schachermayer, TU Vienna)

Erika Hausenblas (University of Salzburg)
SPDEs driven by space time Poisson random measure and its numerical approximation (close abstract)

First, I will give a short account on SPDEs driven by Poisson random measure. The space time Levy noise, or, to be more precise, the space time Poisson random measure will be introduced; existence and uniqueness result will be presented. The second point of the talk will be the numerical approximation by finite elements of the SPDEs aforementioned.

Thorsten Schmidt (University of Leipzig, Germany)
Pricing and Hedging of Credit Derivatives via Nonlinear Filtering (close abstract)

(Joint work with R. Frey and A. Gabih.) This talk considers a new, information-based approach for modelling the dynamic evolution of a portfolio of credit risky securities. In this context, market prices of liquidly traded derivatives are given by the solution of a nonlinear filtering problem. This problem is solved via the innovations approach to nonlinear filtering. Moreover, we derive the ensuing asset price dynamics and compute risk-minimizing hedging strategies. In the last part we discuss a numerical approach - based on particle filtering - to some of the arising filtering problems.

Christa Cuchiero, Start-Seminar,
Affine Interest Rate Models - Theory and Practice (close abstract)

We present the theory as well as the practical applications of affine interest rate models. On the basis of the general theory established by Duffie and Kan, we put emphasis on affine models whose state variables have - in contrast to their theoretical abstract definition - a reasonable economic interpretation. Starting from the very first term structure models, namely the Vasicek and the Cox-Ingersoll-Ross model, we describe in the sequel two- and more-factor models that have appeared in literature. By means of the Vasicek model we exemplify the calibration to market yields as well as to market cap volatilities. However, our main focus are affine yield factor models developed by Duffie and Kan, which allow to relate the state variables to yields with different maturities. We show how to calibrate a two-factor version of this model to market data. The results are promising since the model fits the market yields from different dates very well while the parameters remain nearly constant.

Elena Shmileva
Small ball probabilities of some Lévy processes and their application to the Chung law of iterated logarithm (close abstract)

In this talk, we present some results on probability for a jump Lévy process to stay in a ball of small radius with shifted center. We concentrate our attention on this problem for two classes of Lévy processes: the first consists of the pure jump processes which are close in distribution to the Wiener process, the second is the class of strictly stable processes. We also show what the information on the law of iterated logarithm for these processes is contained in the small ball probabilities results.

Johannes Leitner, Start-Seminar,
Pricing and Hedging with Globally and Instantaneously Vanishing Risk (close abstract)

Using a backward stochastic differential equation (BSDE) approach, we determine in an incomplete market an initial price Y_0 for a non-attainable claim \xi \in L^p, 1 < p < \infty, that takes the hedging risk into account. Y_0 is chosen to be the best price such that the minimal replication error of the optimal hedging strategy with initial capital Y_0 has vanishing risk, the risk being measured with a certain coherent risk measure. This risk measure allows an interpretation as measuring total risk by accumulating instantaneously measured risks. Intertemporal consistency properties of best prices and uniqueness of optimal hedging strategies with vanishing risk are shown. The result can be interpreted as a robust predictable martingale representation property of Brownian motion w.r.t. the intersection of the scenario set defining the risk measure and the set of equivalent martingale measures for the assets traded in the market.

Christer Borell (Chalmers University of Technology, Göteborg, Sweden)
Topics on quasi-concave measures (close abstract)

A positive measure m on a vector space is said to be quasi-concave if m(tA+(1-t)B)>= min(m(A),m(B)) for every real number t between zero and one and measurable sets A and B. In this talk we will review some basic results on quasi-concave measures, here including quite new results by S. Bobkov and M. Ledoux.

Josef Teichmann, Start-Seminar,
New Classes of OU-processes and applications to Optimization procedures

Michel Verschuere (Electrabel Trading and Portfolio Management)
15:30, Sem107
Hedging Under Uncertainty: Applications to Carbon Emissions Markets (close abstract)

We discuss a model for a market with two tradeable asset where the price of the first asset depends on the price of the second asset and the value of an additional source of uncertainty that can not be traded. the source of uncertainty intervenes in the drift of the dynamics defining the price of the second asset. We apply stochastic filtering theory to price the first asset in terms of the second one under the augmented filtration for price and drift component. We illustrate how our model can be applied to markets for EU carbon emission allowances and calculate the value of a digital option on the event that the ETS zone falls short allowances at the end of a trading phase. (Joint work with Umut Cetin of London School of Economics)

Martin Raic (University of Ljubljana, Slovenia)
Stein's Method and Large Deviations (close abstract)

In 1970, Charles Stein developed a new powerful tool for estimating the error in normal approximation, which is, roughly speaking, based on the estimation of the expectation of a suitable differential operator. This approach, nowadays known as Stein's method, turns out to be particularly useful for certain sums of dependent random variables. Important applications include local dependence, finite population statistics and random graphs.
In the present talk, we shall focus on estimating the relative error in large deviation probabilities, i.e., tail probabilities far away from the origin. Under suitable conditions, we shall derive bounds of optimal order.

Zehra Eksi (Middle East Technical University, Ankara)
10:00, Sem107
Comparative Study of Risk Measures (close abstract)

The main aim of this study is to present and compare coherent, convex, conditional convex and some other risk measures both in theoretical and practical settings. Certain emprical findings are also investigated.

Thomas Cass (University of Cambridge)
Smoothness of density for solutions to stochastic differential equations with jumps (close abstract)

We consider solutions to SDEs including a diffusion component and a jump component which is introduced by an integral with respect to a Poisson random measure. We address the question of whether the law of such a solution possesses an infinitely differentiable density under Hoermander's conditions on the vector fields. We show that this is indeed true subject to some restriction on the rate at which the jump measure accumulates small jumps, but which nonetheless permits us to discuss a class of infinite activity jump processes. The central component of the proof is an extension of a classical semimartingale inequality of Norris.

Andreas H. Hamel (University Halle-Wittenberg, on leave ORFE, Princeton University)
A duality theory for set-valued convex functions with applications to set-valued convex risk measures (close abstract)

Duality for extended real-valued convex functions is a well-studied, even classical subject based on works of Fenchel, Moreau, Rockafellar, among many others. A corresponding satisfying theory for functions mapping into the power set of a partially ordered locally convex space is still missing. Such a theory seems to be very desirable since it has already been observed e.g. by Luc in 1989 that the dual of a convex vector optimization problem 'is set-valued in nature'. Moreover, the concept of convex set-valued risk measures has been defined recently in financial mathematics which asks for a corresponding dual representation theory.

We shall present a duality concept that is based on a new notion of affine minorants for set-valued functions and show that almost every concept (e.g. properness, sublinearity, conjugates, inf-convolution) and result (e.g. biconjugation and Fenchel-Rockafellar duality theorems) known in the scalar convex analysis can be established within the new set-valued framework.

A special feature of the methodology is that proofs do not rely on the corresponding scalar theory - as in almost every previous duality theory for vector optimization problems. Finally, we shall show the theory at work when applied to set-valued convex risk measures in order to give dual representation results.

Josef Teichmann, Start-Seminar,
An invitation to random Schrödinger operators V

Alain Desrosieres (INSEE, France), Start-Seminar,
The history of statistics and probability theory as a genre: styles of writing and social uses (close abstract)

Since the beginnig of the 1980's, the history of probability theory and statistics became an important area of research, either by specialists of different disciplines using them (internalist history), or by historians and sociologists (externalist history). The lecture will give a survey on this research, and a comparison between different ways and styles of writing these histories.
Was there a "probabilistic revolution"? It was the question raised in 1983 by a group of researchers coming from several disciplines, during a one year workshop in Bielefeld, Germany, following an idea of a German phycisist, Lorenz Kruger. Was the "Law of large numbers" used in the same way by disciplines like astronomy, physics, economics, political sciences or sociology?

Peter Brandner (BM für Finanzen)
14:00, Seminar Ökonomie der Pensionsfonds,
Reformen in der Altersvorsorge: Theoretische Konzepte aus wirtschaftspolitischer Sicht

Gerald Teschl, Start-Seminar,
An invitation to random Schrödinger operators IV

Peter Imkeller (Humboldt University at Berlin, Germany)
16:30, FH 2
Optimal cross hedging of insurance derivatives,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Franz X. Hof (ECON, TU Wien)
14:00, Seminar Ökonomie der Pensionsfonds,
The Gains from Pension Reform (close abstract)

Assar Lindbeck, Mats Persson: The Gains from Pension Reform, Journal of Economic Literature, Vol. XLI (March 2003), pp. 74-112.
 
Auszug aus der Introduction:
 
Our ambition is not to provide a comprehensive survey of the enormous literature in this field. Instead, we want to highlight some basic principles of pension reform, and to disentangle various efficiency, distributional and stability aspects. To avoid getting bogged down in detail, we base our discussion on a unified analytical framework in the context of a generic overlapping generations model. Such a model automatically focuses on real economic transactions (such as consumption and labor supply), rather than financial recordings (such as government debt). The model also highlights the distribution of income among generations, which is an important aspect of pension systems. The overlapping generations framework allows us to illuminate the fact that many objectives of pension reform could alternatively be brought about by general fiscal policy, i.e., by an appropriate combination of taxes, transfers, and government borrowing ? a point forcefully made in generational accounting (Laurence J. Kotlikoff 2002).
 
After outlining a taxonomy of pension systems (section 2), we briefly discuss the consequences for income distribution, saving, and labor supply of introducing a pay-asyou-go system (section 3). We then address the effects of reforming such a system (section 4). Next, we analyze the consequences of shifting, fully or partially, to an actuarially fair, funded system (section 5). Finally, we discuss risk and the risk-sharing properties of pension systems (section 6). Section 7 offers a brief summary along with examples of recent pension reforms and reform proposals in various countries.

Josef Teichmann, Start-Seminar,
An invitation to random Schrödinger operators III

Pavel Gapeev (WIAS Berlin, Germany)
Constructing jump analogues of diffusions and application to finance (close abstract)

We propose a method for construction of jump analogues of diffusion processes solving stochastic differential equations driven by both a Wiener process and a Poisson random measure, which admit explicit solutions or are reducible to ordinary differential equations. We illustrate the action of this method on some diffusions, which are widely used in finance. We also give some remarks on calculation of the Laplace transforms of the marginal distributions of the constructed jump-diffusions, which are needed for the parameter calibration of the model.

Robert Holzmann (The World Bank, Washington, USA)
14:00, Seminar Ökonomie der Pensionsfonds,
Multi-pillar Pension Reforms: Experience, Lessons, and Challenges (close abstract)

(Vortrag in deutscher Sprache)
The world-wide pension reform dynamics continued into the new millennium and by 2006 31 countries have reformed their pension system toward a multi-pilllar system that includes a mandated and funded pillar. The presentation will review the dynamics, assess the reform directions and lessons, and discuss the challenges ahead. The latter include the capacity to deliver acceptable rates of return in an aging society, the possibility to invest in emerging markets, and the capacity of individuals to make informed decisions.

(Slides)

Juan Pablo Ortega (Université de Franche-Comté, France)
Stochastic Hamiltonian dynamical systems (close abstract)

In this talk I will use the global stochastic analysis tools introduced by P. A. Meyer and L. Schwartz to write down a stochastic generalization of the Hamilton equations on a Poisson manifold that, for exact symplectic manifolds, satisfy a natural critical action principle similar to the one encountered in classical mechanics. Several features and examples in relation with the solution semimartingales of these equations are presented.
Additionally, I will study the case in which the systems presented are invariant with respect to a Lie group action. We will see that in that situation a stochastic version of the Marsden-Weinstein reduction procedure can be carried out, and reconstruction equations can be written down via the use of certain stochastic phase. This is joint work with Joan-Andreu Lázaro.

Johannes Berger (IHS Wien)
14:00, Seminar Ökonomie der Pensionsfonds,
Ten myths about social security reform (J. Stiglitz)

Monique Jeanblanc (Université d'Evry Val d'Essonne, France)
11:15, HS 16
CDS prices in a general case - case of several defaults - hedging strategies (close abstract)

In this talk, we extend the results of the previous one, in a general framework of stochastic intensities. We shall present the case of several defaults, using a dynamic copula approach and we show how the dynamics of a CDS on a default for counterpart 1 are sensitive to the information on the default of counterpart 2. If time allows, we present some hedging strategies.

(Slides)

Monique Jeanblanc (Université d'Evry Val d'Essonne, France)
9:30, HS 14
Hedging defaultable claims: single default (close abstract)

In this talk, we recall briefly the different models of credit risk (intensity based approach and hazard process approach) We characterize the dynamics of a CDS in a simple case of a deterministic intensity. We present different ways to hedge defaultable claims: using no-dividend paying assets (e.g. a corporate bond) and using CDS on a single default.

(Slides)

Josef Teichmann, Start-Seminar,
An invitation to random Schrödinger operators II

Pavel Shevchenko (CSIRO, Sydney, Australia)
Modelling Operational Risk (close abstract)

Many banks adopt a Loss Distribution Approach to quantify an operational risk capital charge under Basel II requirements. Under the Loss Distribution Approach, quantification of the frequency and severity distributions of operational risk involves the bank’s internal data, expert opinions and relevant external data. One of the main challenges in operational risk management is to combine internal data and expert opinion with relevant external data in an appropriate way. Often, in practice, ad-hoc procedures are used to combine these data sources. In this talk we propose a Bayesian inference framework that allows for a combination of these three sources of information to estimate the parameters of the risk frequency and severity distributions.

The talk is based on a paper: D. D. Lambrigger, P.V. Shevchenko and M. V. Wüthrich (2007). The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions. Preprint is available from www.cmis.csiro.au/Pavel.Shevchenko

Gerald Teschl, Start-Seminar,
An invitation to random Schrödinger operators

Sonja Konwicsny (Quelle Lebensversicherung AG, Schwechat)
14:00, FH HS 3
Solvency II (close abstract)

Auf gesamteuropäischer Ebene wird daran gearbeitet die Solvabalitätsvorschriften für Versicherungsunternehmen zu vereinheitlichen und marktwertkonformer und risikoadäquater zu gestalten. Alle diese Bestrebungen sind unter dem Stichwort "Solvency II" zusammengefasst und bekannt geworden. Momentan wird intensiv an einer Rahmenrichtlinie gearbeitet, die die Europäische Kommission (voraussichtlich) am 10. Juli 2007 veröffentlichen wird. Im Vortrag wird ein kurzer historischer Überblick gegeben und auf die (bis jetzt bekannten) Neuerungen zur Berechnung der erfolderlichen Eigenmittelausstattung eines Versicherungsunternehmens eingegangen werden: z.B. Berechnung des Solvenzkapitals (SCR, MCR), der Risikomarge und des Best Estimate. Weiters sollen Chancen und Schwierigkeiten aus Sicht der Praxis diskutiert werden.

Norbert Kirchler & René Knapp (TU Wien, Uniqa)
14:00, Seminar Ökonomie der Pensionsfonds,
The cold war against welfare

Fred Espen Benth (University of Oslo, Norway)
Options and the stochastic volatility model of Barndorff-Nielsen and Shephard (close abstract)

We consider the pricing of options in the stochastic volatility model of Barndorff-Nielsen and Shephard using utility indifference techniqeus. The density of the minimal entropy martingale measure is derived. Based on a numerical solution of a Black-Scholes integro-PDE we find the implied risk aversions for utility indifference pricing using prices quoted on the market. Finally, the Greeks of the options are calcualted based on Malliavin Calculus techniques.

Thomas Url (WIFO)
14:00, Seminar Ökonomie der Pensionsfonds,
Makroökonomische Rückwirkungen des Aufbaus kapitalgedeckter Altersvorsorgesysteme (close abstract)

In kapitalgedeckten Altersvorsorgesysteme transferieren private Haushalte Vermögen durch Ansparen von der Erwerbszeit in den Ruhestand. Während des Ruhestands wird das individuelle Vermögen wieder abgebaut. In einem Sozialversicherungssystem nach dem Umlageverfahren unterbleibt meist der Auf- und Abbau von Kapital, weil die Beitragseinnahmen sofort als Transfers an Pensionisten ausgezahlt werden. Beide Systeme haben makroökonomische Rückwirkungen auf die Arbeitsangebots- und die Sparentscheidung privater Haushalte. Der erwartete demographische Strukturwandel kann diese Effekte verstärken und hat unter Umständen auch Auswirkungen auf die Nachfrage nach Wertpapieren und damit deren Preis- bzw. Ertragsentwicklung. Zu dieser Fragestellung werden einige theoretische und empirische Ergebnisse und einige Simulationsergebnisse aus dem langfristigen Simulationsmodell des WIFO (A-LMM) vorgestellt.

Stefan Tappe (University of Munich, Germany)
13:30, HS 7
Existence of Levy term structure models and invariance problems (close abstract)

The goal of this talk is to provide a characterization of such Levy term structure models admitting a finite dimensional realization (FDR) in terms of the forward rate volatilities. Our starting point is the HJM (Heath, Jarrow and Morton) equation which we regard as one infinite dimensional stochastic equation with values in an appropriate space of forward curves. Under mild regularity conditions on the volatility, we prove the existence of a unique solution. The existence of an FDR is closely related to the existence of an invariant manifold, that is a finite dimensional submanifold on which the solution process proceeds, at least locally. We therefore study invariant manifolds, first for general stochastic equations in infinite dimension driven by Levy processes. Afterwards, for HJM term structure models we derive further conditions on the volatilities for the existence of an FDR. The construction of an FDR in particular situations is considered as well.

Rainer Münz (Erste Bank)
14:00, Seminar Ökonomie der Pensionsfonds,
Pensionskassen in Österreich - Voraussetzungen, Struktur, Begünstigte, verwaltetes Kapital (close abstract)

Allgemein: Pensionskassen dienen der Kapitaldeckung zukünftiger Renten-/Pensionszusagen. Sie haben sich in Österreich im Bereich der betrieblichen Altervorsorge etabliert.
 
Österreich: 2006 gab es in unserem Land ca. 500.000 Arbeitnehmer/innen mit einer betrieblichen Pensionszusage. Relativ am weitesten verbreitet sind solche Pensionszusagen unter Führungskräften (45-55%); seltener bestehen solche Zusagen an Erwerbstätige in anderen Positionen (ca. 13%). Zugleich werden solche Zusagen eher in Großbetrieben und in Branchen mit hohen Durchschnittlöhnen gemacht. Die zukünftigen Begünstigten können dabei u.U. zwischen drei Veranlagungsformen wählen. Daneben gibt es für ca. 85% aller Arbeitnehmer/innen einen obligatorischen Beitrag der Dienstgeber zur jeweiligen Mitarbeiter-Vorsorgekasse.
 
Struktur und Veranlagung: 2006 gab es in Österreich 6 überbetriebliche Pensionskassen sowie etwa 15 betriebliche Pensionskassen. Sie hatten zusammen ein Anlagevermögen von € 12,4 Mrd. Dies entspricht etwa 8% der derzeitigen „funds under management“ österreichischer geschäftsbanken und Versicherungen.

Josef Teichmann, Start-Seminar,
A heat kernel approach to Interest Rate Models (Joint work by Jirô Akahori, Thomas Steiner, Josef Teichmann and Takahiro Tsuchiya) (close abstract)

We construct state price densities by means of a given time-homogenuous Markov process with general state space. These state price densities are applied to construct default-free, Markovian interest rate models. These models share the property of tractability and constitute several completely new and original classes of interest rate models. The article follows the footsteps of the Akahori-Tsuchiya heat kernel approach. The approach can also be seen as another parametrization of Chris Rogers's potential approach. Several examples are calculated and some implementations are shown.

Pavel Grigoriev (University of Leicester, Great Britain)
Risk measures: law-invariance and time consistency (close abstract)

We discuss possible extensions of definitions and results related to law-invariance for time consistent dynamic risk measures.

Ulrike Loy (Allianz)
14:00, Seminar Ökonomie der Pensionsfonds,
Pensionsreformen für Arbeiter und Angestellte ab dem Jahr 2000 und ihre finanziellen Auswirkungen

Ilya Pavlyukevich (Humboldt-University Berlin), Start-Seminar,
Dynamical systems perturbed by heavy-tailed Lévy noise (close abstract)

We consider a one-dimensional dynamical system driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a symmetric \alpha-stable Lévy process, or more generally by a Lévy process with heavy tails. We show that the perturbed dynamical system exhibits metastable behaviour i.e. on a proper time scale it reminds of a Markov jump process taking values in the local minima of the potential U. Finally, we discuss simulated annealing of jump-diffusions driven by \alpha-stable Lévy processes and consider applications to stochastic optimisation.

Wolfgang Woess (TU Graz)
Random configurations driven by random walks

Markus Knell (ÖNB)
14:00, Seminar Ökonomie der Pensionsfonds,
The Optimal Mix Between Funded and Unfunded Pensions Systems When People Care About Relative Consumption

Michael Kupper (ETH Zürich, Switzerland)
Variational Risk Measures on Orlicz Spaces

Christina Ziehaus (Universität Wien)
Variable Selection in the Context of linear Regression (close abstract)

We know that the full linear model is not always the optimal choice, since the usage of all available predictor variables might result in a high variance of the estimated coefficients. If we are willing to accept some bias in the estimates in order to reduce the variance significantly, we might want to choose a smaller model to describe the given problem. Considering all possible different models can be time consuming, therefore we need an automatic search procedure to find a reasonable small number of possible models we can consider and compare in detail.
Besides discrete methods of forward and backward selection, which will produce different models depending on the chosen stopping criterion, we will also consider continuous processes.
Ridge regression and LASSO are well known methods of this kind. The most promising technique is the LARS estimation which is not only fast, but can be adapted to provide solutions of LASSO and forward stagewise regression. All the methods are described in detail, and connections between them will be presented.
Finally, the different methods are used to analyze a given dataset and the results are compared.

Martin Keller-Ressel, Thomas Steiner
Yield Curve Shapes and the Asymptotic Short Rate Distribution in Affine One-Factor Models (close abstract)

We consider a model for interest rates where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic, Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate r_t. We give conditions under which the short rate process will converge to a limit distribution and describe the limit distribution in terms of its cumulant generating function. We apply our results to the Vasicek model, the CIR model, a CIR model with added jumps and a new model of Ornstein-Uhlenbeck type.

Jiro Akahori (Ritsumeikan University, Japan)
Antisymmetric Malliavin calculus and its applications (close abstract)

First I will construct "wedge" product in the Wiener space, then by standard "Bosonization" procedure I will introduce "derivative" and "integration by part" which are quite different from the ones appearing in (symmetric) Malliavin calculus. I will then explain how these notions are related to interest rate modelling.

Gerald Teschl (Universität Wien)
16:00, Start-Seminar,
Random Schroedinger Operators on one foot (close abstract)

Random Schroedinger operators arise in the quantum mechanical description of crystals which are perturbed by randomly inserted impurity atoms (think of the doping process in semiconductor devices) or in the study of quasi-crystals. I will try to give a brief introduction to this subject using the so called Anderson model.

Thorsten Schmidt (University of Leipzig, Germany), Start-Seminar,
The Term Structure of CDO Losses (close abstract)

This paper directly models the forward term structure of losses of a CDO in a Heath-Jarrow-Morton like way and derives conditions under which the model is free of arbitrage. We also analyze the relationship of different securities and consider the pricing of derivatives on CDOs. This is joint work with D. Filipovic and L. Overbeck.

Antonis Papapantoleon, Start-Seminar,
Semimartingales and Lévy processes in finance: duality and valuation (close abstract)

The first part of this talk will concentrate on the duality principle in option pricing, in a general semimartingale framework. Roughly speaking, the duality principle states that the price of a call option for a model with price process S = exp(H) (w.r.t. a measure P) is equivalent to the price of a put option for a suitable dual model S' = exp(H') (w.r.t. a dual measure P'). We also give applications to exotic options in Lévy models. The second part of the talk will concentrate on valuation methods for vanilla and exotic derivatives. We will pay special attention to options that depend on the supremum of a Lévy process.

Paweł Polak (Warsaw University, Poland)
Immunization of the insurance portfolio under random interest rates (close abstract)

It is gone be assumed that assets and liabilities are stochastic processes and that regulatory demands on solvency are satisfied under basic time structure of interest rates. There gone be shown the lower bounds on change in the portfolios present value when the interest rates change randomly (in two cases when the portfolio is not correlated with time structure of interest rates and when it is correlated). These bounds will be used to immunize the portfolio valuation when arbitrary changes of interest rate scenarios are considered. An example of application of the results will be given (construction of optimal funding method for defined benefit pension plans).

Nikolaos Georgiopoulos (Vienna Graduate School of Finance)
Real Options Valuation under expected utility maximization (close abstract)

Real Options have been on the spot of academic research for the last ten years, since they are able to combine managerial flexibility along with traditional discounted cashflow valuation. This enables firms to integrate strategy and finance on a sound basis. Central to the theory of Real Options is pricing when the underlying asset is not traded as it happens in most of the cases. A naïve approach would be to try to find a surrogate asset which is traded and exhibits correlation with the non traded, and use no-arbitrage arguments to price the option. Although intuitionally plausible, Hubalek and Schachermayer (2001) showed that no-arbitrage does not convey any information regarding the price. In this setting of a traded and a non traded correlated asset, I present an approach by Henderson and Hobson (2002) based on utility maximization of terminal wealth. An analytic formula is derived under the assumption that the exposure to the non traded asset is relatively small with respect to total wealth. I also present another approach using the Hamilton Jacobi Bellman equation which gives similar results but in a more tractable way, which will also be a basis of future extensions.
Finally I discuss some possible extensions to the model, plus another attempt to price and hedge these non traded claims.

Richard Warnung
Stable Recurrences for Risk Aggregation (close abstract)

We consider the loss of an insurance portfolio in a one period model. Dependence among subportfolios is modeled such that the portfolio loss can be decomposed into independent components that have the form of (discrete) compound mixed-Poisson random variables. Due to this form it is possible to calculate the distribution of the aggregate loss by the famous Panjer algorithm or by a recursive expansion of the probability generating function (pgf) of the aggregate loss. Starting from known recurrences we derive new, numerically stable, recurrences and apply them to the pgf resulting from various mixing distributions as well as to the calculation of risk contributions. (Joint work with Stefan Gerhold)

Catherine Rainer (Université de Brest, France)
11:00, Sem 107
Stochastic differential games with asymmetric information (close abstract)

We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some second order Hamilton-Jacobi equation.

Takahiro Tsuchiya (Ritsumeikan University, Kusatsu, Japan)
What is the natural scale for a Lévy process in modelling term structure of interest rates?

Nicolas Privault (Université de Poitiers, F)
Convex comparison inequalities for exponential jump-diffusion processes (close abstract)

Given M and N respectively a forward and a backward exponential martingale with jumps and a continuous part, we prove that E[f(M(t)N(t))] is non-increasing in t when f is a convex function, provided the local characteristics of the stochastic logarithms of M and of N satisfy some comparison inequalities. As an application, we deduce bounds on option prices in markets with jumps, in which the underlying processes need not be Markovian. In this setting the classical propagation of convexity assumption for Markov semigroups is not needed.

Maria Siopacha
Taylor Expansions of Option Prices (close abstract)

We apply methods from Malliavin calculus to study the approximation of option prices. We are interested in stochastic differential equations, which depend on a parameter and are built in a general hypoelliptic framework. Our main theorem is the existence of weak Taylor approximation schemes of any order. We work out weight expressions for the Taylor coefficients of the expansion. We apply our methodology to LIBOR market models in order to deal with the typical stochastic drift and with stochastic volatility. We obtain accurate and tractable option pricing formulas. Our results are underlined by numerical evidence. (Joint work with Josef Teichmann)

Tom A. Ashu (University of Kaiserslautern, Germany)
Asset Liability Management for Pension funds using Conditional Value at Risk constraints (close abstract)

An efficient model for finding optimal contribution rates and portfolio allocation takes into consideration the funding situation of the Pension fund. To include this in our model we can construct it as a multi period asset liability management model. One may borrow ideas from multi period portfolio optimization to find optimal solutions. Hibiki (2001b,2003) proposed an alternative stochastic programming model with simulated paths called the hybrid model. The advantage of the hybrid model with simulated sample paths is that the simulated path structure compared to the tree structure gives a better accuracy to describe uncertainties of parameters and the hybrid structure adds flexibility in the decisions.

In my Masters thesis, I use CVaR risk measure to formulate linear programming problems in the asset liability management for pension funds. I propose the application of Ward’s method on the total Liability measure to be met by the Pension fund to construct a hybrid model as described in Hibiki (2001b, 2003). The Hybrid model obtained does not distort the linearity or convexity of the problem as found in Uryasev (2001).

Fabrice Baudoin (Université Paul Sabatier, Toulouse)
Chen series and Atiyah-Singer theorem (close abstract)

The purpose of this talk is to provide a new and short proof of the Atiyah-Singer local index theorem for the Dirac operator on the spin bundle. The method relies on approximations of heat semigroups constructed from truncations of Brownian Chen series.

Thomas Wenger
(Westfälische Wilhelms-Universität Münster, at the moment: consultant)
Perturbative methods in algebra and finance: are there any relations? (close abstract)

Perturbative methods seek to solve equations of various kinds (polynomial, differential or other) via first solving problems which are in a suitable sense 'close' to the original problem and then trying to perform some asymptotic expansion (or deformation) with the hope of obtaining information about the original problem. As such, these techniques have found wide applications and their usefulness is both highly intuitive and witnessed by their enormous success, for example in physics. Interestingly, such methods do not only apply in problems of analysis (with the Taylor expansion as paradigm case) but have also proven helpful in algebra and number theory. For a long time, various practices and toolkits have coexisted in various research communities that equally thrived on these techniques. In recent time, some systematic efforts have been carried out to unify these approaches and to make visible the underlying principles, also to some extent explaining the wide applicability. Since the methods have been successfully and diversely implemented already, the point of such an abstract exercise naturally lies in trying to find new, previously unexploited ranges of application - apart from leading to an increased economy of thought.
The aim of the talk is to report on some new points of view on constructions relevant in finance, which have emerged as a result. One perennial theme which underlies these observations is (maybe unsurprisingly) the occurrence of tree-indexed summation schemes in the context of perturbative approaches. These have recently been proved to support a lot more structure than visible at first glance. It is this fact which makes the search for new relations potentially fruitful. At this time, these relations may still seem somewhat coincidental, but it can be argued that from a principled point of view they need not come as a surprise. For example, relations exist in the study of parametrized families of copulas and for various aspects of 'skew' or 'smile' modelling of implied volatilities or implied correlations in the context of derivatives.

Martin Keller-Ressel, Michael Kupper
Equilibrium Pricing (close abstract)

We introduce a new class of preferences over discounted wealth evolutions and show the existence of equilibria. We give a formula for the equilibrium transition densities and discuss examples when the agents measure their risk with Beta-VAR or p-AVAR, respectively. The equilibrium density can be used for option pricing and gives a partial explanation for the high risk premia for in-the-money options ('volatility skew') that are observed in the market. It is the joint work with Patrick Cheridito (Princeton University) and Damir Filipovic (LMU Munich).

Tomas Björk (School of Economics, Stockholm)
Optimals Investment under Partial Information (close abstract)

We consider optimal investment problems where the local rate of returns of the assets under consideration are driven by a process $X$ which cannot be observed directly. The problem is that of finding the optimal portfolio strategy which maximizes the utility of terminal wealth, under the constraint that the portfolio has to be adapted to the filtration generated by observations of the asset price vector $S$ only, whereas $X$ is onobservable. This leads to an optimal control problem under partial information. For various special cases, problems of this kind has earlier been successfully studied by Brennan, Bäuerle, Rieder, Brendle, Nagai, Runggaldier and others. The contribution of the present paper is that we study a fairly general problem without any assumptions of a markovian structure. Within this framework we obtain fairly explicit formulas for optimal wealth and optimal portfolio stratgies. The existing results in the literature then come out as easy special cases of the general theory. (Joint work by Tomas Björk & Mark Davis & Camilla Landen)

Mark Davis (Imperial College London, UK)
16:30, FH 2
Dynamic models for portfolio credit risk,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Eva Farkas (Erste Bank)
16:30, FH 2
Copulae - Modellierung des gemeinsamen Verhaltens von Risikofaktoren in der modernen Finanz- und Versicherungsmathematik,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Mark Podolskij (Ruhr-University of Bochum)
17:30, FH 2
Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps (close abstract)

We propose a new concept of modified bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modified bipower variation is proven. Under further assumptions we prove stable convergence of our estimates. Moreover, we construct estimates which are robust to finite activity jumps.

Ole E. Barndorff-Nielsen (University of Aarhus)
16:30, FH 2
Volatility and Power Variation,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

G. Komaromi, C. Schoenherr, U. v. Aufschnaiter (Credit Suisse, London)
12:00, HS 17 Friedrich Hartmann
Investment Banking: What is it all about? (close abstract)

Gewinnen Sie einen Überblick über die unterschiedlichen Bereiche einer Investment Bank und lernen Sie insbesondere das Fixed Income Geschäft näher kennen.

Wir bieten wir Ihnen die Möglichkeit einen Eindruck der folgenden Geschäftsbereiche zu gewinnen:

• Interest Rate Products, Swaps Trading
• Tax, Accounting & Regulatory Structuring

Anschliessend, ab ca. 13 Uhr: Informationen für Studierende und AbsolventInnen:
Wir bieten Ihnen Einblicke in die Kultur unseres Unternehmens, unsere Geschäftsbereiche und unterschiedliche Einstiegsmöglichkeiten. Wir stellen Ihnen den Bewerbungs- und Einstellungsprozess im Investment Banking Geschäft vor und erläutern, wie Sie sich erfolgreich bewerben können. Weitere Informationen über die Einstiegsmöglichkeiten in die Credit Suisse finden Sie unter www.credit-suisse.com/standout.

Stefan Gerhold
16:15, SEM 104
Automatisches Beweisen von Identitäten
Vortragsreihe: Wissenswertes der Mathematik, details

Kasper Larsen (Carnegie Mellon University)
15:00, SEM 104
Stability of utility-maximization (close abstract)

The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets as well as investor's preferences. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of these input parameters lead to only small changes in the agent's optimal behavior derived from the solution of the related utility-maximization problems.

Laszlo Gyorfi (Budapest University of Technology and Economics)
Empirical portfolio selection (close abstract)

The purpose of this seminar is to show sequential investment strategies that guarantee an optimal rate of growth of the capital under minimal assumptions on the behavior of the market. The theoretical results show that the asymptotic rate of growth matches the optimal (log-otimal) one that one could achieve with a full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The empirical results show that the performance of the proposed investment strategies measured on past NYSE data is solid, and sometimes even spectacular.

Benedikt Blum (TU München)
15:00
Deterministic Pricing of Options on Lévy driven Assets (close abstract)

Exponential Lévy asset models are an essential extension to the standard Osborne/Samuelson/Black/Scholes market model. Here the problem of pricing European options can be expressed by a partial integro-differential equation (PIDE) analogous to the Black-Scholes-PDE with the Lévy-Khinchine-triplet as the only input about the driving process. Such a parabolic PIDE can be treated efficiently by a wavelet Galerkin discretization in space and a finite-difference-scheme in time. The corresponding mass/stiffness matrices have to be compressed to sparse due to the nonlocal nature of the integral operator.
Unlike most other methods this one can be extended to american style options as well as to more general processes (e.g. sochastic volatility).

Christian Litterer (Oxford University)
10:30, Sem 107
High order recombination and an application to Cubature on Wiener Space (close abstract)

Higher order particle methods can provide an accurate description of an evolving family of measures, but frequently the number of particles used in the description explodes as we iterate. We present a general method to simplify the support of the intermediate measures used in the iteration without increasing the error in the particle approximation by more than a constant factor. We describe two algorithms that can be used to simplify the support of a discrete measure and give an application to the cubature on Wiener space method developed by Lyons, Victoir.

Gregor Dorfleitner (WU Wien)
Coherent risk measures, coherent capital allocations, and the gradient allocation principle (close abstract)

The gradient allocation principle, which generalizes the most popular specific allocation principles, is commonly proposed in the literature as a means of distributing a financial institution's risk capital to its constituents. This presentation is concerned with the axioms defining the coherence of risk measures and capital allocations, and establishes results linking the two coherence concepts in the context of the gradient allocation principle. The following axiom pairs are shown to be equivalent: positive homogeneity and full allocation, subadditivity and "no undercut", and translation invariance and riskless allocation.
Furthermore, we point out that the symmetry property holds if and only if the risk measure is linear. As a consequence, the gradient allocation principle associated with a coherent risk measure has the properties of full allocation and "no undercut", but not symmetry unless the risk measure is linear. The results of this paper are applied to the covariance, the semi-covariance, and the expected shortfall principles. We find that the gradient allocation principle associated with a non-linear risk measure can be coherent, in a suitably restricted setting.
Furthermore some considerations regarding the economic relevance of risk capital allocation are presented.

PRisMa 2006
One-Day Workshop on Portfolio Risk Management

Petra Posedel (Università Bocconi, Milano)
Asymptotic analysis for a simple explicit estimator in BNS stochastic volatility models (close abstract)

We examine the joint time series of logarithmic returns and the instantaneous variance. In the BNS setting the asymptotic theory of estimators from martingale estimating functions is obtained. Specifically, results about existence of consistent estimators and about asymptotic normality of these are given. Moreover, the optimality of such estimators is proved. This is joint work with Friedrich Hubalek.

Miklos Rasonyi
Optimal investment under transaction costs (close abstract)

This is an occasion to present the results of Davis and Norman from their 1990 (!) paper: trading in a Black-Scholes stock market but under proportional transaction costs the form of the optimal trading policy is given and an algorithm to determine its parameters is provided (there are no explicit formulas for them).

Stefan Gerhold
13:00
An Implementation of the LIBOR Market Model (close abstract)

The LIBOR market model is the standard model for pricing interest rate derivatives. I explain how the model is set up and how it can be calibrated to caps, swaptions, and historical interest rate data. Then I present an application of the model to the pricing of a structured note on the spread between two swap rates.

Stefan Gerhold
10:00
Crashcourse Interest Rate Models (close abstract)

The main goal of the talk is to explain the short rate models by Vasicek, Hull-White, and Black-Derman-Toy. I briefly explain what risk neutral valuation is and what the basic building blocks of the models are, viz. short rates and zero coupon bonds. Then I outline how the models are set up, calibrated, and implemented. Finally, I summarize what little there is in the literature concerning advice on model choice.

Mathias Zocher (TU Dresden)
16:30, FH 2
Multivariate gemischte Poissonprozesse - Bonus-Malus-Systeme in der KH-Versicherung,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Pavel Shevchenko (CSIRO Mathematical and Information Sciences, Sydney)
15:00
Modelling Operational Risk (close abstract)

A significant part of uncertainty in a firm’s earnings is related to the way it operates business in terms of operational risk that cannot be explained by market fluctuations. Under Basel II requirements, the banks should hold a capital against operational risk. The banks are allowed to use internal models for operational risk quantification. However, they should demonstrate the accuracy of internal models within 56 Basel II risk cells (eight business lines times seven risk types). The models should make use of internal data, relevant external data, scenario analysis and factors reflecting business environment and internal control systems. Emerging best practices share a common view that Loss Distribution Approach (based on modelling of frequency and severity of operational risk losses) is the soundest method. Quantification of operational risk is a relatively new area when compared to quantification and understanding of credit and market risks. Creation of meaningful quantitative approach to operational risk management is a difficult task with many challenges emerging. Different opinions on measurement techniques and methodologies are hotly debated. In this talk we address several important aspects of operational risk modelling using Loss Distribution Approach such as: combining expert opinions with historical data; modelling data thresholds; dependence between risks.

Martin Keller-Ressel
Non-Parametric Calibration of the Barndorff-Nielsen-Shephard Model (close abstract)

The Barndorff-Nielsen-Shephard model is a model for asset-price evolution that includes both a diffusion part with stochastic volatility and a jump part that is driven by a Levy-process. The market implied by this model is not complete and in the risk-neutral case the model can be described by four parameters: The average volatility, its rate of mean-reversion, a leverage parameter that models a dependency effect between volatility and price movements and a Levy measure that represents the intensity and size of jumps.

To calibrate this model we are trying to infer the model parameters from an array of (European) option prices of different strikes and maturities, which we assume are traded liquidly in the market. The idea is that once the model is calibrated it can be used to price more complicated derivatives.

For the calibration we do not assume a specific distibutional form of the Levy density, hence we speak of non-parametric calibration. This calibration problem is an ill-posed inverse problem, such that regularization techniques have to be employed. Also the problem is computationally intensive such that one has to think carefully about implementation and optimization issues.

Alexander Cherny (Moscow State University)
11:00, Sem 105B
Coherent Risks and their applications (lecture series) (close abstract)

The basic idea behind these lectures is: the whole finance can be built based on coherent risks.

I will speak about applications of coherent risks to:

• pricing;
• optimization;
• optimality pricing;
• equilibrium.

Moreover, several topics in the "pure" theory of coherent risks will be discussed. These include:

• coherent risk contribution;
• capital allocation;
• factor risks.

I will also describe two new classes of coherent risks: Alpha V@R and Beta V@R that are better than Tail V@R.

These lectures will be based on a series of papers available at: http://mech.math.msu.su/~cherny/ (papers 24-30).

Oliver Fiala (Erste Bank)
16:30
Estimation and Comparison of Credit Transition Matrices (close abstract)

In credit risk management, migration or transition matrices (expressions are used simultaneously) are major inputs for risk management, Credit Risk figure calculation, derivative pricing, etc. First I will elaborate a little bit on how to come to a transition matrix fitting given rating data published by Lando and Skodeberg. Later on I will introduce some distance measures for different transition matrices including a newer one developed by Trück and Rachev. They provide criteria for measuring the impact of differences in transition matrices on risk figures and show that generally used metrics are not able to capture that.

Alexander Cherny (Moscow State University)
17:15
Coherent Risks and their applications (lecture series) (close abstract)

Alexander Cherny

The basic idea behind these lectures is: the whole finance can be built based on coherent risks.

I will speak about applications of coherent risks to:

• pricing;
• optimization;
• optimality pricing;
• equilibrium.

Moreover, several topics in the "pure" theory of coherent risks will be discussed. These include:

• coherent risk contribution;
• capital allocation;
• factor risks.

I will also describe two new classes of coherent risks: Alpha V@R and Beta V@R that are better than Tail V@R.

These lectures will be based on a series of papers available at: http://mech.math.msu.su/~cherny/ (papers 24-30).

Alexander Cherny (Moscow State University)
11:00, FH 2
Coherent Risks and their applications (lecture series) (close abstract)

The basic idea behind these lectures is: the whole finance can be built based on coherent risks.

I will speak about applications of coherent risks to:

• pricing;
• optimization;
• optimality pricing;
• equilibrium.

Moreover, several topics in the "pure" theory of coherent risks will be discussed. These include:

• coherent risk contribution;
• capital allocation;
• factor risks.

I will also describe two new classes of coherent risks: Alpha V@R and Beta V@R that are better than Tail V@R.

These lectures will be based on a series of papers available at: http://mech.math.msu.su/~cherny/ (papers 24-30).

Andreas H. Hamel (Universität Halle-Wittenberg)
Fenchel conjugation for set-valued convex functions and applications to set-valued risk measures (close abstract)

The biconjugation theorem of Convex Analysis is an essential tool to prove representation theorems for convex (especially coherent) measures of risk. It says that every proper, convex and closed function on a locally convex space does coincide with its Fenchel biconjugate. Especially, every such function has a continuous affine minorant.

We shall investigate convex functions with values in partially ordered locally convex spaces and in power sets of such spaces. It will turn out that it is more natural even for vector-valued functions to consider set-valued affine minorants and set-valued Fenchel conjugates rather than vector-valued ones. We shall establish a biconjugation theorem for the set-valued case and derive a representation theorem for set-valued convex measures of risk.

However, there is a series of serious questions: What do properness, closedness and convexity mean for set-valued functions? What is a set-valued affine minorant, in what sense does it minorize a set-valued function and how shall we define the pointwise supremum of such objects? These questions will be answered affirmatively using order relations on the power set of an ordered linear space.

More detailed abstract with formulas

Preprint: "Translative Sets and Functions and their Applications to Risk Measure Theory and Nonlinear Separation"

Johannes Leitner
16:15, SEM 104
Optimale Portfolios mit 'lower partial moment constraints'
Vortragsreihe: Wissenswertes der Mathematik, details

Nicole Bäuerle (Universität Karlsruhe)
16:30, FH 2
Portfolio-Optimierung bei Sprung-Diffusionsprozessen mit unbeobachtbarer Sprungintensität,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Klaus D. Schmidt (TU Dresden)
12:30, FH 2
Multivariate Modelle und Methoden in der Schadenreservierung (close abstract)

Die neuere Entwicklung der Mathematik der Schadenversicherung ist geprägt durch eine starke Tendenz zu einer multivariaten Betrachtungsweise. Im Gegensatz zu univariaten Modellen, die ausschließlich Eigenschaften einzelner Bestände beschreiben und Abhängigkeiten zwischen verschiedenen Beständen ignorieren, können in multivariaten Modellen genau diese Abhängigkeiten dargestellt werden. Dies gilt auch für die Schadenreservierung.

Der Vortrag stellt den Übergang zur multivariaten Betrachtungsweise anhand von zwei klassischen Modellen der Schadenreservierung dar. Beide Modelle - das multivariate additive Modell und das multivariate Chain-Ladder Modell - sind lineare Modelle. In beiden Fällen sind daher Ergebnisse über optimale lineare Prognosen anwendbar.

Handouts (PDF 265 KB)

Klaus D. Schmidt (TU Dresden)
16:30, FH 2
Bornhuetter-Ferguson & Co.:
Eine Familie von Verfahren der Schadenreservierung,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Klaus D. Schmidt (TU Dresden)
12:30, FH 2
Lineare Prognosen und Schadenreservierung (close abstract)

Gegenstand der Schadenreservierung ist die Bestimmung von Reserven für Schäden, die noch nicht bekannt oder noch nicht vollständig abgewickelt sind (Spätschäden).

Die Schadenreservierung verfügt über ein umfangreiches Arsenal von Methoden, die meist in der Praxis entstanden sind und damit zunächst einen heuristischen Charakter besitzen. Aus statistischer Sicht, die dem zufälligen Charakter der Spätschäden Rechnung trägt, können diese Methoden als stochastische Prognose-Verfahren interpretiert werden. Damit stellt sich die Frage nach der Variabilität der Prädiktoren. Diese Frage kann nur durch die Begründung der Prädiktoren durch ein geeignetes stochastisches Modell beantwortet werden.

Der Vortrag gibt einen Überblick über lineare Prognosen im linearen Modell und in verschiedenen Credibility-Modellen sowie einige Beispiele für Anwendungen in der Schadenreservierung.

Handouts (PDF 197 KB)

Karel Janecek (RSJ Invest, Prague)
Optimal investments with proportional profit-share fee: Analysis of the high-water-mark fee structure (close abstract)

The objective of this paper is to find an optimal investment strategy for the case where an investor pays profit share to an investment manager (for example a hedge fund). We assume that upon investing into a hedge fund, the size of agent's total investment is followed, and a provision is charged whenever the total accumulated profit exceeds the historical maximum - the so-called high water mark. We assume that the agent holds a CRRA utility function and maximizes a value function of consumption. We derive the HJB equation for this problem. As expected, the optimum consumption proportion is lower than the Merton proportion. The results are somewhat intriguing as far as the optimal investment proportion is concerned. We provide numerical results for several interesting cases.

Stefan Gerhold
The current state of the OeBFA module of the CD laboratory (close abstract)

The Austrian Federal Financing Agency (OeBFA) collaborates with TU Vienna in a new module of the Christian Doppler Laboratory for Portfolio Risk Management (PRisMa Lab). I give a brief outline of the goals of this module and discuss the basics of an approach to compute the present value of exotic swaps in OebFA's portfolio.

Michael Hanke (Universität Innsbruck)
16:30
Structural Credit Risk Models Beyond Merton: Solutions via PDEs vs. Change-of-Numeraire (close abstract)

Recently, a new strand of the literature on structural credit risk models evolved. It differs from the classical models in two important ways: First, instead of an exogenous firm value process, these models are based on an exogenous cash-flow process. Second, geometric Brownian motion is replaced by alternative processes, in particular arithmetic Brownian motion and "reverse" geometric Brownian motion. Closed-form solutions have been derived via solution of PDEs. Using the change of numeraire approach, the existence of closed-form solutions in these cases is - at least - not immediately obvious.

Umut Cetin (London School of Economics)
15:30
An equilibrium model for default risk (close abstract)

(Joint work with Luciano Campi.) We study an equilibrium model for the pricing of a defaultable zero coupon bond in the framework of Back (1992). The market consists of an informed agent, noise traders and a market maker who sets the price using the total order. We find the equilibrium pricing rule for the market maker, explicitly calculate the default intensities and show that in the equilibrium the total order process behaves like a Bessel bridge from insider's point of view while the insider's trades cannot be detected by the market.

Uwe Schmock (FAM, TU Vienna)
Stein's method for proving the central limit and the Berry-Esséen theorem

Yuliya Bregman (Universität München)
Estimation of multivariate ruin probabilities (close abstract)

We consider the estimation of the ruin probability in an insurance risk portfolio. We model the claims in different dependent business activities by some multivariate regularly varying compound Poisson process. We model the dependence of the components by a Lévy copula. We show how Lévy copulas can be used to construct examples of multivariate regularly varying compound Poisson processes. Finally, we illustrate our method by analyticl approximation of the ruin probability in a Clayton-Pareto model.

Yuxin Yang (New York University)
14:00
A brief survey on copulae (close abstract)

I'll present the concepts of copula and quasi-copula, their basic properties and relationships with some measures of stochastic dependence/association. I'll also cover a few useful families of copula as well as some examples of financial applications.

Henryk Zaehle (Allianz PKV-AG, München)
Heat equation with strongly inhomogeneous noise (close abstract)

The object of interest is the heat equation with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous with respect to the Lebesgue measure, neither in space nor in time.

In the first part of the talk, we explain the precise meaning of this equation and we present results on existence, uniqueness and non-negativity of continuous solutions. In the second part of the talk, we consider the equation in connection with branching particle systems.

Gabriel Maresch (TU Wien)
Hartman measurability and unique mean values (close abstract)

A group G is called amenable if there exists a finitely additive translation invariant probability measure on the powerset of G. In most interesting amenable groups, including the integers and the real numbers, such a measure is neither sigma-additive nor unique. Hence the situation here is almost, but not quite, entirely unlike the situation of compact groups where normalized Haar measure exists.

Half-Day Workshop
on Credit Risk and Risk Transfer
(Freihaus Hörsaal 3, 2pm to 6pm)

Susanne Klöppel (ETH Zurich)
Utility based good deal bounds (close abstract)

Via utility maximization we obtain a criterion which specifies a set of reasonable pricing measures. For any untraded payoff this set implies price bounds tighter than the no arbitrage bounds. We study the price bounds as processes. Their computability and dynamic properties depend on the set of pricing measures. Thus the aim of this talk is to give an appropriate definition for this set.

Markus Petermann (Converium)
11:00 in seminar room 105
Measures of Risk and Run-off of Portfolios (close abstract)

Adjusting the risk capital of a multi-period run-off portfolio over time is a problem that, in our opinion, is not really dealt with by the multi-period risk measurements proposed in the literature. Motivated by this problem we propose a different look at one-period risk measures: A one-period portfolio is renewed until the investor opts to exit, whereby the accepted exit-times are assumed to be elements of a predefined set T of stopping times. The risk capital is defined as the minimal amount needed to ensure that in the average the run-off is covered, irrespective of the investor's exit-strategy. We show that most coherent risk measures can be represented in this way. We examine VaR, worst conditional expectation and expected shortfall in this light. Finally, we argue that the approach has potential to be generalized to the multi-period case.

Irina Slinko (Stockholm School of Economics)
On Finite Dimensional Realizations of the Two Country Interest Rate Models (close abstract)

In this paper we study a two country economy and model a financial market where the domestic T-bonds, the foreign T-bonds as well as the exchange rate derivatives are traded. We use the Heath-Jarrow-Morton approach, modelling domestic and foreign forward rates directly under each country martingale measure. Thus, the interest rate setting for both countries is defined by two infinite dimensional stochastic differential equations (SDEs). The purpose of the paper is to understand when the inherently infinite dimensional domestic and foreign forward rate processes can be realized by means of a Markovian finite dimensional state space model.

We assume that forward rate volatilities as well as the volatility of the exchange rate can be arbitrary smooth functionals of both forward rate curves. We find necessary and sufficient conditions in terms of the exchange rate and interest rate volatilities to ensure that we obtain a finite dimensional realization (FDR) for both domestic and forward interest rates and we show how the exchange rate depends on such realizations. Finally, for the case when FDRs exist we show how to derive the dynamics of the underlying factors spanning the state space.

Rafal Lochowski (Warsaw University)
HJM model driven by Levy process (close abstract)

The talk is mainly based on the paper "HJM condition for models with Levy noise" by J. Jakubowski and J. Zabczyk. A generalization of HJM model is considered, in which the forward curves are driven by a Levy process with values in a separable Hilbert space instead of Wiener process in a finite dimensional real space. It is of special interest to find conditions on the forward rate process, under which the discounted bond price processes are local martingales. The aim of the talk will be to give necessary and sufficient conditions, in terms of characteristics of Levy process, implying that discounted bond price processes are local martingales and to derive the HJM condition. It will turn out that model implies existence of the exponential moments of the noise processes.

Stefan Gerhold (Universität Linz)
Special Functions: Applications of Computer Algebra in Stochastics (close abstract)

Linear recurrence relations and linear ordinary differential equations with polynomial coefficients provide a unified framework for the algorithmic treatment of a large class of special functions. We present some applications of recent algorithms to stochastics, e.g. symbolic calculations involving probability density functions and probability generating functions.

Andreas Hula (TU Wien)
Nonarchimedean Functional Analysis (close abstract)

The talk will give a general view of functional analysis over nonarchimedean fields. The main focus will be on differences and similarities to the archimedean case. Eventually the nonarchimedean spectral theorem can be treated too.
The talk will be in german.

Paolo Guasoni (Boston University)
Consistent Prices and Face-lifting Pricing under Transaction Costs (close abstract)

Consistent Price Systems (CPS) are the counterparts of martingale measures for models with transaction costs, as they guarantee the absence of arbitrage, and allow to characterize superreplication prices of contingent claims. Unfortunately, and especially for non-semimartingale models, the explicit calculation of CPS is not always immediate.

We first establish the existence of CPS for price processes endowed with their natural filtration from a condition on their topological support, which can often be easily verified. In particular, we see that any two nonatomic continuous processes with full and support have the same set of consistent price systems.

We then exploit this result to characterize the superreplication prices of a class of contingent claims as the backward recursive concave envelope (face-lifting) of their payoff. For European calls and puts, we obtain a very simple proof that their prices are trivial.

Johanna Neslehova (RiskLab, ETH Zurich)
Modeling Dependence of Non-Continuous Random Variables and Compound Poisson Processes
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Mesrop Janunts (Institut für Mathematik, TU Berlin)
Duality methods for portfolio optimization (close abstract)

The talk is mainly based on the paper "The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets" by D. Kramkov and W. Schachermayer.

The problem of maximizing the expected utility of the terminal wealth in the framework of a general incomplete semimartingale model of a financial market is considered. It is shown that the necessary and sufficient condition on a utility function for the validity of several key assertions of portfolio optimization hold true if we require the asymptotic elasticity of the utility function to be strictly less than one.

Walter Fisher (IHS Institute for Advanced Studies, Vienna)
Relative Wealth and Endogenous Employment: A Short- and Long-Run Analysis (close abstract)

This paper introduces a specification of instantaneous preferences in which status depends on relative wealth. In contrast to the relative consumption framework, we show that under relative wealth preferences it is not necessarily the case that agents supply an excessive amount of labor in steady-state equilibrium. Using a specific parameterization, we also examine the initial behavior of the economy and find that agents consume too little and work too hard compared to a situation in which status considerations do not a play a role.

Birgit Rudloff (Martin-Luther-Universität Halle-Wittenberg)
Convex Hedging in Incomplete Markets and Generalizations (close abstract)

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures. The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. The optimal strategy consists in superhedging the modified claim φH, where H is the payoff of the claim and φ is the solution of the static optimisation problem, the optimal randomized test.

In this talk, we will deduce necessary and sufficient optimality conditions for the static problem using convex duality methods. The solution of the static optimisation problem turns out to be a randomized test with a typical 0-1-structure.

The results can be generalized to solve the hedging problem for a more general class of risk measure. Furthermore, we can apply these results to the problem of testing compound hypothesis. We show that the obtained results extend previous results in test theory.

Damir Filipovic (LMU München)
16:30, FH 8
Equilibrium and optimality for monetary utility functions under constraints (joint with Michael Kupper)
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Uwe Schmock (FAM, TU Vienna)
Presentation of the New Christian Doppler Laboratory on Portfolio Risk Management (close abstract)

We outline the basic idea of Christian Doppler laboratories as a way to promote precompetitive, applied research cooperations between universities and the Austrian industry. We then present the newly approved laboratory for Portfolio Risk Management (PRisMA), a joint venture of the research group for financial and actuarial mathematics at the TU Vienna and its founding industry partner Bank Austria Creditanstalt. A short introduction to the envisioned research modules will be given by the respective module leaders.

Hans Buehler (Deutsche Bank London und TU Berlin)
Variance Swap Market Models (close abstract)

We introduce a new approach for pricing and hedging in equity markets.

The idea is to model the dynamics of the term structure of variance swap prices and the stock price together. We therefore introduce an HJM-type framework which we spezialize to the case of curves which are driven by a finite-dimensional Markov process. We discuss issues of market completeness and present a few examples and implications on the recalibration of stochastic volatility models.

Miklos Rasonyi (Hungarian Academy of Sciences)
Convergence of utility prices to the superreplication price (close abstract)

In this talk we look at the behaviour of the reservation prices as agents' risk-aversion tends to infinity. We show in discrete-time market models that under suitable conditions they converge to the superreplication price. This extends previous results for exponential utilities.
 
We discuss the limitations of our approach and some pathologic cases which arise if we try to relax our assumptions.
 
This is joint work with Laurence Carassus.

Lange Nacht der Forschung:
Von A wie Aktie bis S wie Sterbewahrscheinlichkeit
17:00-24:00, Freihaus der TU Wien

PRisMa 2005
One-Day Workshop on Portfolio Risk Management
(HS 16 Karl von Terzaghi Hörsaal, Main Building of TU Wien)

Thorsten Schmidt (Universität Leipzig)
Credit Risk - Incomplete Information (close abstract)

We consider the pricing of corporate securities when the investors do not have full information. On one side, one can consider a random default boundary, such that even if the firm value was known, the time of default would not be predictable. On the other side, investors have no access to the true firm value. We will propose an approach which takes this into account and consider consequences to the pricing of equity and debt.

Umut Cetin (London School of Economics, UK)
Modelling liquidity effects in discrete time (joint work with Chris Rogers) (close abstract)

We study optimal portfolio choices for an agent with the aim of maximising utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox-Ross-Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.

Beatrice Acciaio (University of Perugia, Italy)
Optimal Risk Sharing and Mean-Variance Principle (close abstract)

We study the problem of optimal risk sharing among n agents endowed with choice functionals which are non-necessarily monotone. In particular, we consider the mean-variance principle and we compare it with its most conservative monotone approximation. Some examples with explicit characterization of the solutions are also given.

Mihai Sirbu (Columbia University, NY)
Risk-Tolerance Wealth Processes and Sensitivity Analysis of Utility Based Prices (joint work with D. Kramkov) (close abstract)

In incomplete markets the prices of contingent claims can only be established taking into account the preferences of the agent. This leads to the well known definition of (marginal) utility based prices. Representing the price of a unit of contingent claim as a function of the number of claims q, we perform an asymptotic expansion around q=0. The key element of the analysis turns out to be the existence of the risk-tolerance wealth process. This will be the natural numeraire for the asymptotic analysis. The presentation is based on joint work with Dmitry Kramkov.

Pavel Grigoriev
No Arbitrage and Equivalent Martingale Measures In Illiquid Markets (joint work with U. Cetin) (close abstract)

In a joint work of U. Cetin and P. Grigoriev a model of market with illiquidities (i.e. a market with convex transaction costs) was studied. For this model the No Arbitrage was characterized as absence of arbitrage in so-called “relevant economies” which are a sequence of markets with proportional transaction costs. Thus Using the Fundamental Asset Pricing Theorem for the relevant economies we establish that No Arbitrage for the market with illiquidities is equivalent to the existence of a sequence of probability measures which are in some sense an analog of the classical martingale measure for a frictionless market.

Peter Grandits
16:00 s.t.
Optimal Expected Exponential Utility of Dividend Payments in a Brownian Risk Model (joint work with F. Hubalek, W. Schachermayer and M. Zigo) (close abstract)

We consider the following optimization problem for an insurance company
\max_{C}\E \left[ U\left( \int_{0}^{\infty}e^{-\beta t}dC_{t}\right)\right].
Here $C$ denotes the accumulated dividend process, $U$ an exponential utility function and $\beta$ a discounting factor. We prove that the optimal strategy is a barrier strategy, provided the risk aversion parameter in the utility function is small enough. The barrier function is described as a solution of a certain integro-differential equation.

Reinhold Kainhofer
16:15 in seminar room 104
Quasi-Monte Carlo Methoden -- Am Schnittpunkt von numerischer Analysis, Zahlentheorie und Finanzmathematik
Vortragsreihe: Wissenswertes der Mathematik, details

Jürgen Hartinger (Graz University of Technology)
Rare Events - Monte Carlo and Quasi-Monte Carlo Methods (joint work with Dominik Kortschak) (close abstract)

Recently, there has been much interest in developing Monte Carlo methods for estimating rare event probabilities. The reason seems to be two-fold: The topic is of major interest in areas such as credit and insurance risk or telecommunication networks and presents a challenge from methodological point of view as naive methods lead to ineligible variances for the estimates. After an overview on existing methods in a Monte Carlo setting, in this talk we focus on theoretical and empirical aspects of (randomized) QMC methods in rare event sampling.

Grigory Temnov
Risk models with stochastic premium income (close abstract)

We investigate a risk model that extends the classical risk process. In this model a total claim amount process is considered to be the same as in the classical model while a premium income is a stochastic process unlike the classical case. A formula for a ruin probability of an insurance company with this risk process (analog of the Beekman convolution formula) is derived and the comparison of the two models in terms of ruin probabilities is made. Prospects of the application of investigated model as the model of financial strictures, such as currency exchange business, are discussed. The further generalizations of the investigated model with respect to its applicability in the real situations are outlined. Methods used in this part are similar to the ones that had been initially developed for classical risk process, such as the use of the Cox processes for the modeling the number of claims within a time interval instead of Poisson process. Achieved by other authors results of investigations of this model, main of which are the derivation of the bounds for the ruin probability (analog of the Lundberg inequality) and the asymptotic estimates for it with the growth of the initial capital, are described. Finally, the essential aspects of the problem of computation the ruin probability function for the model with random income, as well as for the classical model, are investigated. That part of the work is based mainly on the use of the Fourier methods that allow to simplify the procedure of the calculation of ruin probability substantially. The numerical results of the evaluation of ruin probability are presented. The accuracy of the proposed calculation scheme is investigated.

Luciano Campi
A hedging theorem under transaction costs (close abstract)

We prove a general version of the super-replication theorem, which applies to Kabanov's model of foreign exchange markets under proportional transaction costs. The market is described by a matrix-valued c\`{a}dl\`{a}g bid-ask process $(\Pi_t)_{t\in [0,T]}$ evolving in continuous time. Specifically, we propose a new definition of admissible portfolio processes as predictable (not necessarily right or left continuous) processes of finite variation related to the bid-ask process by some economically intuitive relations. Under the assumption of existence of a Uniformly Strictly Consistent Price System (USCPS), which is the uniform version of a well-established concept, we prove a closure property for the set of attainable vector-valued contingent claims. We then obtain the super-replication theorem as a consequence of that property, thus generalizing to possibly discontinuous bid-ask processes analogous results obtained in \cite{K}, \cite{KL} and \cite{KS}. Rasonyi's counter-example \cite{R} served as an important motivation for our approach.

Peter Friz (Statistical Laboratory, University of Cambridge)
Levy's Area under Conditioning and Applications (close abstract)

First, we show that the Hoelder-norm of Brownian motion is small when the Brownian motion is conditioned to be uniformly small. Then we find that under the same conditioning a suited Hoelder norm of the Levy-area is also small. Jointly, these results say that the Hoelder norm of the Brownian rough path is small under uniform conditioning. The full support theorem for diffusions is a direct corollary. This is joint work with T. Lyons and D. Stroock. Time permitting, I will mention other developments in the field.

Christian Bayer
17:00, Sem 107
An elementary proof of Tchakaloff's Theorem (about a joint work with J. Teichmann)

Josef Teichmann (Technical University of Vienna)
Calculation of Greeks with jumps (joint work of Barbara Forster, Eva Luetkebohmert and Josef Teichmann) (close abstract)

We show partial integration results for jump diffusions in a very traditional way, i.e. without applying partial integration on Poisson spaces. The key result is to find a bound for the p-norm of the inverse of the Malliavin derivative.

Dietmar Pfeifer (Carl von Ossietzky Universität Oldenburg)
16:30, FH 6
Zur Bedeutung der Modellierung abhängiger Risiko-Prozesse für die europäische Versicherungswirtschaft
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Dmitry Rokhlin (Rostov State University, Russia)
On some problems of no-arbitrage: constructive criteria in the case of finite discrete time and the Kreps-Yan theorem (close abstract)

The first problem concerns the first fundamental theorem of asset pricing under portfolio constraints. We prove an appropriate extended version of the Dalang-Morton-Willinger theorem. In particular, the market no-arbitrage is characterized in terms of supports of price increments conditional distributions. The proposed approach uses the theory of measurable multivalued maps and relies on the well-known results for an ideal market.
Another problem is connected with the no-arbitrage on the market with transaction costs. We call it martingale selection problem. For a multivalued stochastic process with an open convex values $G_n(\omega)$, defined on a filtered probability space, we provide the existence criterion of the following pair:
an adapted single-valued process, whose elements $S_n$ are selectors of $G_n$, and an equivalent martingale measure for $S$. This criterion is expressed in terms of supports of regular conditional upper distributions of $G_n$.
We also discuss the Kreps-Yan theorem, allowing another approach to the existence of equivalent martingale measures and no-arbitrage. The new version of this theorem for the case of $L^\infty$ is proved.

Alexandra Dias (Credit Suisse and ETH Zurich)
16:30, FH 6
Copula change-point detection and dynamic copula models for multivariate high-frequency data in finance
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Daniel Dvorak
An Extension of Panjer's Recursion (close abstract)

Sundt and Jewell have shown that a nondegenerate claim number distribution Q = {q_n}_{n \in N_0} satisfies the recursion
q_{n+1} = (a + b/(n + 1))*q_n
for all n \in N_0 if and only if Q is a binomial, Poisson or negativebinomial distribution. This recursion is of interest since it yields a recursion for the aggregate claims distribution in the collective model of risk theory when the claim size distribution is integer-valued as well. A similar characterization of claim number distributions satisfying the above recursion for all n \in N_0 with n >= 1 has been obtained by Willmot. In the present paper we extend these results and the subsequent recursion for the aggregate claims distribution to the case where the recursion holds for all n \in N_0 with n >= k for arbitrary k \in N_0. Our result are of interest in catastrophe excess-of-loss reinsurance.

Stefan Ankirchner
Enlargement of filtrations, continuous Girsanov-type embeddings and utility maximization of insiders (close abstract)

Let $(\cG_t)$ be an enlargement of the filtration $(\cF_t)$. Jeulin and Jacod discussed a sufficient criterion for the inheritance of the semimartingale property when passing to the larger filtration. We provide alternative proofs of their results in a more general setting by using decoupling measures and Girsanov's changes of measure. We derive necessary and sufficient conditions for the embedding of vector spaces of $(\cF_t)$-semimartingales into spaces of $(\cG_t)$-semimartingales to be continuous in terms of generalized entropies of the information increment. Finally we apply these results to the calculation of the maximal expected utility of an investor with additional information.

Reinhold Kainhofer
Zur Erstellung der österreichischen Rententafeln AVÖ2005R

Walter Schachermayer
Optimal Design of Risk Exchange for Cash-Invariant Risk Measures

Eva Lütkebohmert (Department for Probability Theory and Statistics, University of Bonn)
Hypoellipticity in Infinite Dimensions for the Jump Diffusion Case (close abstract)

We consider an infinite dimensional stochastic differential equation driven by a Q-Wiener process and a Poisson process. In the case where the Lie algebra generated by the coefficients of the stochastic differential equation is finite dimensional it has been shown that there exist finite dimensional realizations in the sense of Bjørk, Filipovic, Teichmann, et al.. We study here the case where the Lie algebra is assumed to be dense in the underlying (infinite dimensional) Hilbert space. Under this condition we show that the law of the solution process when projected to the Euclidean space Rⁿ admits a density with respect to the Lebesgue measure on Rⁿ. Hence we extend the result of Baudoin and Teichmann to the general jump diffusion case. The main result is based on a Malliavin calculus for the jump diffusion case. For this we define two derivative operators, one with respect to white noise and the other one with respect to the Poisson process. We then obtain an infinite dimensional version of Hörmander's theorem on the product space.

Thomas Dockal (Generali Holding Vienna AG, Controlling - Riskmanagement)
Allokation von Risikokapital in Versicherungsportfolios (close abstract)

Der Vortrag fasst eine Diplomarbeit und ein Paper von Michael Urban (TU München) zusammen, der sich mit der Allokation von Risikokapital in Versicherungsportfolios beschäftigt hat.

Es werden für die Allokation Risikomaße und Allokationsmethoden vorgestellt und deren Eigenschaften diskuttiert und versucht eine "Bewertung" vorzunehmen.

Nicolas Victoir (Oxford University)
A Short Introduction to Rough Paths and Applications to Numerical Analysis (close abstract)

A short introduction to Rough Paths will allow us to present the algorithm "Cubature on Wiener space", which offers a new way of approximating weakly SDEs. The method consists of replacing the Wiener measure by a linear combination of Dirac measures, which means that our solution is approximated by a weighted average of solution of ordinary differential equations. We give some applications to Option pricing.

Irene Klein (Uni Wien)
No Market Free Lunch and Large Financial Markets (part 2) (close abstract)

Motivated by the uniform version of NMFL for the class U2 of non- decreasing concave functions on a 'small market' I introduce a uniform version of No Asymptotic Market Free Lunch on a large financial market. I show that for the class U2 the uniform version of NAMFL and NAMFL are equivalent and, moreover, equivalent to No Asymptotic Free Lunch (which is the analogous result for large financial markets as the result in the talk before). Moreover, I use the uniform version of NAMFL to prove a version of the Fundamental Theorem of Asset Pricing for large financial markets.

Irene Klein (Uni Wien)
No Market Free Lunch and Large Financial Markets (part 1) (close abstract)

Fritelli (2002) introduced the notion No Market Free Lunch (NMFL) which is a no free lunch condition depending on the preferences of the investors in the market (which are given by equivalent probability measures and utility functions in a certain class U). He showed the relations between NMFL and No Free lunch with Vanishing Risk and between NMFL and No Arbitrage. Moreover he presented a version of the Fundamental Theorem of Asset Pricing based on NMFL. In the talk I show that NMFL with respect to the class U2 consisting of all non-decreasing concave functions on the real line can be replaced by a uniform version of NMFL. Using some facts on Orlicz spaces I show that NMFL (and the uniform version) are equivalent to No Free Lunch. Moreover I present a NMFL condition for a large financial market (No Asymptotic Market Free Lunch, NAMFL) and show the connection with various forms of No Asymptotic Arbitrage Conditions.

Josef Teichmann
Calculation of the Greeks by Cubature Formulas II (close abstract)

We continue by presenting both cubature formulas as recipes and providing the basic steps for the proofs.

Michel Verschuere (Risk Analyst, Luminus Hasselt and FAM @ TU Wien)
Optimal forward investment in power markets (close abstract)

Supply and demand for power needs careful matching at all times, as electricity cannot be stored once it is generated. One of the most important tasks for every transport grid operator consists (TGO) in the offering of such 'balancing services'. As demand levels prove sometimes difficult to predict even the day before, TGO's must keep sufficient reserve capacity online to cope with unforeseen deviations from expected consumption.

Balancing services have an intrinsic cost attached to them, but TGO's often maintain a financial penalty system with the objective to encourage market participants' improved forecasting performance. In this seminar, we first sketch the balancing penalty systems currently of use in the UK and Belgian market environment.

From the model perspective, we discuss a simple market where an investor tends to cover a random future demand level using forward contracts, whose dynamics becomes increasingly volatile as the instant of physical delivery closes in. The investor has all reasons to cover his supply obligations as good as possible, in order to avoid the unattractive balancing regime. At the end of the day, we arrive at an optimal investment problem that allows for treatment using known results from stochastic optimization theory. We particularly look for solution properties of the Hamilton-Jacobi-Bellmann equation.

Alexander McNeil (ETH Zurich)
Some New Copulas for Risk Modelling
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Philippe Clement (TU Delft)
R-Boundedness and Operator-valued Multipliers (close abstract)

In this lecture we shall introduce the notion of R-bounded family of operators in a Banach space. Recently many new results in the theory of operator-valued multipliers (of Marcinkiewicz, Mihlin or Schur type) have been obtained by using this new notion of boundedness. Connections with the problem of Lp-maximal regularity for abstract differential equations in Banach spaces will also be considered.

Josef Teichmann
Calculating the Greeks by Cubature formulas (close abstract)

We provide Cubature formulas for the calculation of derivatives of expected values. The exposition starts with an introduction of the meanwhile classical approach of Lyons/Victoir. We then formulate the problem for the calculation of Greeks for a given process and apply this analysis to the cubature problem.

Traian Pirvu (Carnegie Mellon)
Satisfying Convex Risk Limits by Trading (close abstract)

A random variable, representing the final position of a trading strategy, is deemed acceptable if under each of a variety of probability measures its expectation dominates a floor associated with the measure. The set of random variables representing pre-final positions from which it is possible to trade to final acceptability is characterized. In particular, the set of initial capitals from which one can trade to final acceptability is shown to be a closed half-line . Methods for computing a are provided, and the application of these ideas to derivative security pricing is developed.

Pavel Grigoriev
Representation of "dilatation monotonous" or "co-monotonic additive" risk measures (capacities) (with J.Leitner) (close abstract)

We study the special class of coherent risk measures which satisfy an additional property called "dilatation monotonicity" (monotonicity with respect to taking conditional expectations over arbitrary sub sigma algebras). This property appears to be natural for at least 2 reasons: First, the conditioned random gain is "more determined" than the original one and so it should be less risky; second, all risk measures which are consistent with respect to utility maximization over all utility functions are dilatation monotonous.

In particular, we proved that the dilatation monotonicity is equivalent to so-called "co-monotonic additivity". In the case of atomless probability space the dilatation monotonicity implies the risk measure is also law invariant. Among the other results we characterized the extreme points of the set of scenario probabilities for dilatation monotonous coherent risk measures.

Giovanni Cesari
Counterparty Credit Exposure for Exotic Derivatives
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Walter Schachermayer, 16:30-16:45
Stimmgewichtung in der EU

Anca Antonov
Performance of Modern Techniques for Rating Model Design (close abstract)

The usual qualitative assessment of individual risks of borrowers, other than individuals, relies on ratings. Due to the current emphasis on extensive data on individual borrower's risks, modeling became attractive for assessing risk in a comprehensive and objective manner, and for complying with the New Accord recommendation. There are several generations of models of credit risk and default probabilities, starting with the early statistical models linking ratings to financial characteristic of the firms, up to elaborate econometric technique, neural network models or based on Merton's model.

The scope is to test the efficiency and the accuracy of statistical approach: logistic regression,discriminant linear and quadratic analysis, polynomial regression, k-nearest neighbours, Parzen window density comparing with different types of neuronal networks(multilayer perceptrons, radial basis, learning vector quantization, or selforganized maps). It emphasis on finding the most appropriate measure for the generalization performance (on the never seen data), as well as the link between the classical statistical models and neural networks.

Michel Verschuere
Risk management in immature electricity markets (close abstract)

We address a selection of problems that typically arise in young power markets. The talk was prepared for with the present day structure of the Belgian market in mind. Partial deregulation was achieved there on July 1st 2003, when the Flemish retail market fully opened for competition. However, the Flemish market is currently in a transition phase, as its structure still resembles to the regulated environment. Production in Belgium is highly concentrated to just one incumbent, OTC forward trading is very illiquid and there is no spot market as yet.

Risk management in this highly restrictive environment proves to be a challenging task and it is my intention to give an eye-witness account of its every day practice during this talk.
 

Fulvio Pegoraro
Pricing and Inference with Mixtures of Conditionally Normal Processes (close abstract)

(Joint work with Henri Bertholon and Alain Monfort)
We consider the problems of inference and derivative pricing when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases the risk-neutral processes and explicit pricing formulas are obtained.
 

Daniel Straumann (ETH Zurich)
Parameter estimation in conditionally heteroscedastic time series models. (close abstract)

This talk deals with the estimation in certain conditionally heteroscedastic time series models, such as e.g. GARCH, asymmetric GARCH or EGARCH. By exploiting the techniques of stochastic recurrence equations, we develop a general and unifying limit theory for the maximum-likelihood estimator (MLE) and quasi-maximum likelihood estimator (QMLE) in a certain parametric class of conditionally heteroscedastic time series models. This generalizes and clarifies work of Lumsdaine (1996) and Berkes et al.(2003). We furthermore discuss the issue of misspecification in the MLE and the behavior of the QMLE in the presence of a heavy-tailed noise distribution. A second part of the thesis studies the asymptotic behavior of the classical Whittle estimator when it is applied to the squares of GARCH(1,1). We focus on the case of an unconditional distribution with an infinite 8th moment and thereby generalize results by Giraitis and Robinson (2001).
 

Reinhold Kainhofer
19:30, Österreichische Studienförderungswerk Pro Scientia, Mezzanin, Währinger Straße 2-4, 1090 Wien
"Lebensräume - Lebensträume" sich erfüllen und absichern: Ein Streifzug durch die Grundlagen aus Finanz- und Versicherungsmathematik (close abstract)

Ich werde (hoffentlich) allgemein verstaendlich erklaeren, was Versicherungs- und Finanzmathematik ueberhaupt ist, und wofuer wir das machen. Zuerst werde ich die Versicherungsmathematik vorstellen, wobei ich neben einer Vorstellung verschiedener Versicherungstypen auch darauf eingehe, dass die dahinterliegenden Daten modlliert werden muessen (Sterbetafeln etc.). Der zweite Teil beschaeftigt sich mit Finanzmathematik und wir nach einer Vorstellung verschiedner Typen von Derivaten auf die Grundlagen und einige leicht verstaendliche Modelle eingehen. Abschliessend schneide ich auch noch kurz die numerische Simulation an.

Wie gesagt, der Vortrag richtet sich an Nicht-Mathematiker, also werde ich alle Dinge moeglichst ohne Formeln und nur mit Handwaving-Argumenten erklaeren.

Anna Rita Bacinello
16:30, FH 6
Modelling the Surrender Conditions in Equity-Linked Life Insurance
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Laurence Carassus
Existence of a particular martingale measure for models displaying "the stationarity assumption" (close abstract)

We consider investment models with infinite time horizon but such that each investment ends in a finite time. The investment's set is supposed to be "stable" in the sense that every investment available today should be available at the same conditions in the future. This assumption is called stationarity. Intuitively the "stability" of the investment's set should imply some nice property on the dual set of martingale measures. We will recall the results obtained for deteministic and binomial markets. We will also enlight some difficulties which appear when the set of the sample space is infinite.

Alexander Cherny
General Arbitrage Pricing Model: Probability and Possibility Approaches (close abstract)

We present a general arbitrage pricing model. It includes as particular cases

• static as well as dynamic models;
• models with a finite number of assets as well as those with an infinite number of assets;
• models related to market risk as well as those related to credit risk;
• models with no transaction costs as well as those with transaction costs;
• models with no costs of short selling as well as those with costs of short selling or with short selling prohibited;
• combinations of various models.

Within the framework of the general arbitrage pricing model, we obtain

• the Fundamental Theorem of Asset Pricing;
• the form of fair prices of a contingent claim;
• the form of fair prices of a controlled contingent claim (this notion is introduced in the paper).

2. The obtained general results are applied to several particular models (one-period model, multiperiod model, continuous-time model, etc.). The "projection" of general results on these models leads us, in particular, to the revision of the Fundamental Theorem of Asset Pricing in the continuous-time case: the proposed variant of this theorem states that the absence of the generalized arbitrage is equivalent to the existence of an equivalent measure, with respect to which the discounted price process is a martingale (not just a sigma-martingale). In the model with the infinite time horizon, the uniformly integrable martingales come into play.

3. The general approach mentioned above allows us to narrow considerably the class of equivalent risk-neutral measures (and thus to make the intervals of fair prices shrink) by taking into consideration the current prices of traded securities (options, bonds, etc.).

4. Furthermore, the obtained results are extended to models with friction, i.e. models with

• proportional transaction costs;
• restrictions on short selling;
• costs of short selling.

5. Finally, we introduce the possibility approach to pricing by arbitrage. When using this approach, one does not need to know the original probability measure. It is shown that all the results described above can be transferred to the possibility framework.

Dirk Tasche
Konzentrationssensitive Kapitalanforderungen für Kreditrisiken
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Luciano Campi
Hedging for an insider in incomplete markets

Gallus Steiger (ETH Zürich)
On the optimal martingale measure for exponential utiity indifference pricing (close abstract)

Let us consider a locally bounded asset process S as well as a contingent claim B which fulfills some integrability conditions. By the duality theorem of convex optimization, the dual problem of an investor with exponential utility (with risk parameter \alpha) is to minimize
      -exp {E_Q[\alpha B]-I(Q,P) }
over all martingale measures, whereas I(Q,P) stands for the relative entropy.

Let us assume that the price process S is driven by a Jump-diffusion process Y. Many researchers have been discussing the nature of the optimal martingale measure for specific cases. One can identify two main areas where results have been developped. The first case is when the asset process is modelled by some Levy process. However, results are only known for the case when B is set to zero, i.e. the optimal martingale measure is the so-called Minimal Entropy Martingale Measure. On the other hand, also stochastic volatility models have been analyzed, but restricted to the case where the asset process is assumed to be a continuous semimartingale and the jumps appear only in the volatility process.

The purpose of this talk is to present a new technique which allows to extend the results to the case where one allows both the contingent claim B to be nonzero as well as jumps to appear in the asset process. Effectively, this technique allows to identify the optimal martingale measure for a wide asset class of jump-diffusion models. We show two examples, namely the optimal martingale measure in case of Levy processes for the case B not equal zero as well as the Minimal Entropy Martingale Measure in the Barndorff-Nielsen Shephard model.
 

Uwe Schmock (16.00 im Seminarraum 104)
Einführung in die Kreditrisikomodellierung, Vortragsreihe: Wissenswertes der Mathematik, details

Bulat Khaydarov (Attention: this talk starts at 17:30)
Market Liquidity and Its Effect on Portfolio Risk

Karel Janecek
Futures Trading Model with Transaction Costs

Carlo Sgarra
An exact analytical solution for discrete Barrier Options obtained via a Wiener-Hopf Factorization (close abstract)

The talk will present an analytical solution to the pricing of discrete barrier options in the Black-Scholes framework. The problem is reduced to an integral equation of convolution type which is possible to solve with a classical Wiener-Hopf factorization technique. A comparison of the solution obtained with other solutions already available in the literature obtained by numerical methods is provided.
The results have been obtained in joint work with G. Fusai of the Avogadro University (Novara) and D.I. Abrahams of the Manchester University.
 

Mesrop Janunts
Duality methods for portfolio optimization (close abstract)

The talk is mainly based on the paper "The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets" by D. Kramkov and W. Schachermayer. The problem of maximizing the expected utility of the terminal wealth in the framework of a general incomplete semimartingale model of a financial market is considered. It is shown that the necessary and sufficient condition on a utility function for the validity of several key assertions of portfolio optimization hold true if we require the asymptotic elasticity of the utility function to be strictly less than one.
 

17:00-18:00 Umut Cetin
An Alternative Proof of Fundamental Theorem of Asset Pricing with Proportional Transaction Costs (close abstract)

I'll try to give a, somewhat rigorous, sketch of the proof of the fundamental theorem in the setting of Jouini and Kallal (1995) using arguments from utility maximization.
 

Pavel Grigoriev
On low dimensional Case in the Fundamental Asset Pricing Theorem with Transaction Costs

Umut Cetin
A Very Simple Model for Liquidity Risk

Alexander Schied
Optimal investments for robust utility functionals (close abstract)

We introduce a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model, where the robust utility functional is defined by a set $\cQ$ of probability measures. Our main result shows that this problem can be reduced to determining a "least favorable" measure $Q_0\in\cQ$, which is universal in the sense that it does not depend on the particular utility function. Then the robust problem is equivalent to a standard utility maximization problem with respect to the \lq\lq subjective" probability measure $Q_0$. By using the Huber-Strassen theorem from robust statistics, it is shown that $Q_0$ always exists if $\cQ$ is the core of a 2-alternating capacity. We also discuss the problem of robust utility maximization with uncertain drift in a Black-Scholes market and the case of "weak information" as studied by Baudoin (2000).
 

Alexander Uljanov (16:30 im Besprechungszimmer 107, Freihaus, 6.OG, grün)
Fondsgebundene Lebensversicherungen mit Mindestgarantie (close abstract)

Fondsgebundene Lebensversicherungen mit Mindestgarantie (FLVG) sind außerordentlich wichtig für die neue private Zukunftsvorsorge und Abfertigung neu, da diese Produkte auf FLVG basieren.
FLVG stellt zur Zeit größte Herausforderung für österreichische Versicherungsunternehmen sowohl in aktuarieller als auch in praktischer Hinsicht dar.
Hauptproblem besteht hier in Entwicklung von effizienten Methoden der Garantieabsicherung/Leistungsmaximierung auf Einzelnvertragsebene.
Es wird eine einzelvertragliche Absicherungsstrategie präsentiert, die folgende Vorteile hat:
• Dynamische Strategie, die Absicherungskosten werden über die ganze Vertragslaufzeit verteilt und erst dann "bezahlt", wenn sie notwendig sind
• Möglichkeit einer internen IT-Lösung auf Basis vorhandener technischen Bestandsverwaltung (Module für Reserveberechnung, Kostenverwaltung, Vertragsänderungen usw.)
• Laufende Optimierung der Vertragswerte
• Stornobekämpfung durch neue höhere Garantie
• Kostenersparnis in Rückversicherung, externen Dienstleistungen, Garantiegebühren
• Keine Absicherungsprämie im voraus, keine Finanzierung
• Stabiler Cash Flow
• Niedrigere Sollvabilitätserfordernisse als in Hybridprodukten
 

Josef Teichmann
Generalising the Hobson-Rodgers model (close abstract)

joint work with Friedrich Hubalek and Robert Tompkins

We provide a generalisation of the well-known complete stochastic volatility models by David Hobson and Chris Rodgers, which capture smiles of for instance the british pound market. Since those models are driven by hypoelliptic stochastic differential equations, particular care is needed in order to calculate prices, hedging ratios, etc. In order to navigate around the difficulties of inverse problems for partial differential euqations we provide a numerically stable approximation of prices by methods of partial integration. It is particularly nice that - even though the involved equations are complicated - the relevant approximation terms appear to be integrals of polynomials in Gaussian variables.
 

Josef Teichmann (16.00 im Seminarraum 118)
Geometrie der Zinsen, Vortragsreihe: Wissenswertes der Mathematik, details

Andreas Kull
'Solvency II': Ein neues Aufsichtsmodell für die Versicherungswirtschaft in der EU
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Josef Teichmann
Cubature on Wiener Space from the point of view of central limit theorems (close abstract)

joint with Fabrice Baudoin

In the framework of Cubature formulas on Wiener Space a relation to central limit theorems (or more precisely invariance principles) is analysed. We provide a formula in the spirit of central limit theorems, which reveals this relation nicely. Several aspects of applications to mathematical finance are discussed, since the resulting numerical schemes for the approximation of expected values preserve the relevant invariance properties of mathematical finance, for instance the approximating tree is a martingale.
 

Peter Friz
Rough Path and Stochastic Analysis

Umut Cetin
Trading in Illiquid Markets (close abstract)

Classical theories of financial markets assume infinitely liquid markets. We study an illiquid market where price paid/received depends on the size and the timing of the trade. The prices are not necessarily moved by a large trader. Dependency of the price on the trade size comes from the imbalance between the supply and the demand for the asset. Hence, classical models become a special case. We first find the self-financing condition in presence of illiquidities and see that the self-financing condition restricts the set of allowed trading strategies, i.e. not all predictable trading straegies can be used. We then study conditions for no arbitrage. Since the set of feasible strategies is shrunk and there is furthermore a liquidity cost, the market is no longer complete even if there exists a unique martingale measure for the "marginal price" of the asset. However, we can get an approximately complete market when the martingale measure is unique. In this incomplete market we study the problem of optimal investment.
 

Stefan Geiss
Approximations of European type pay-offs, fractional Sobolev spaces, and random time nets

Filip Lindskog (ETH Zurich)
On regular variation for stochastic processes (close abstract)

We study a formulation of regular variation on the space of R^d-valued right-continuous functions on [0,1] with left limits and provide necessary and sufficient conditions for a stochastic process with sample paths in this space to be regularly varying. A version of the Continuous Mapping Theorem is proved which enables the derivation of the tail behavior of rather general mappings of the regularly varying stochastic process. For a wide class of Markov processes with asymptotically independent increments we obtain simplified sufficient conditions for regular variation. For such processes we show that the possible regular variation limit measures concentrate on step functions with one step, from which we conclude that extremes for such processes are due to one big jump. Finally, using the Continuous Mapping Theorem we derive the tail behavior of filtered regularly varying Markov processes with asymptotically independent increments. For illustration we study the tail behavior of an Ornstein-Uhlenbeck process driven by a regularly varying Levy process.
 

Jörn Sass
Portfolio Optimization under Partial Information (close abstract)

We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return (drift process) modeled as an unobserved continuous time, finite state Markov chain. The investor wishes to maximize the expected utility of terminal wealth. Partial observation means that for his investment decisions only the prices are available to him.

While the optimal terminal wealth and the existence of an optimal strategy are known in a quite general setting, it is not possible to determine an optimal trading strategy explicitly without specifying a model for the drift process.

We give an overview of some recent results and then motivate our continuous time Markov chain model for the drift which leads to a hidden Markov model (HMM) for the stock returns. An explicit representation of the optimal trading strategy in terms of the unnormalized filter of the drift process can be derived using HMM filtering results and Malliavin calculus.

Aspects of parameter estimation, simulation, and application to historical prices will be discussed. For the latter we show how the extension to non-constant volatilities can improve the optimization results considerably.
 

Tom Fischer (13:00-13:45, Sem 107)
An axiomatic approach to valuation in life insurance

Reinhold Kainhofer
Entwicklung sublinearer Dividendenmodelle und deren numerische Behandlung (close abstract)

In meinem Vortrag werde ich die Erweiterung der klassischen Ruinmodelle mit (konstanten bzw. linearen) Dividendenschranken auf sublineare Schranken vorfuehren. Im Speziellen werde ich nicht- bzw. konstant verzinste Ruinprozesse in Verbindung von Barrieren der Form (b^m+t/alpha)^(1/m) mit Konstanten a,b>0, m>=1 betrachten. Die resultierenden nicht-linearen partiellen Differentialgleichungen koennen nicht elementar geloest werden, weshalb wir einen Integraloperator definieren, dessen Fixpunkt gesucht ist. Dieses Problem wird numerisch mit verschiedenen Quasi-Monte Carlo Methoden geloest.
 

Elmar Teufl
Oszillationen im Zusammenhang mit dem Sierpinski Graph und dem Sierpinski Dreieck (close abstract)

Wir werden verschiedene Resultate für den Sierpinski Graphen und das Sierpinski Dreieck diskutieren, bei denen logarithmische Oszillationen auftreten: die Größe von geodäsischen Kugeln, Eigenwertstatistik des Laplace-Operator, verschiedene Größen der einfachen Irrfahrt bzw. der Brownschen Bewegung.
 

Michel Verschuere
Tackling the Forward Cascade in Power Markets (close abstract)

We formulate a valuation method for futures derivatives in realistic power markets. The presence of the forward cascade there may seriously limit hedging attempts for futures options when the underlying remains hidden in the market. Our approach relies upon statistical evidence collected from the European Energy eXchange presented in an earlier talk. This is joint work with Lutz von Grafenstein.
 

Lutz von Grafenstein
A Model for Electricity Futures Prices (close abstract)

We present the state of art of a model developped by Michel Verschuere, Martin Schaden and myself. In our ansatz we try to explain certain features of electricty futures prices by identifying 'micro-economical' quantities which drive the price evolution. implications for option pricing in electricity markets and open problems are discussed.
 

Michel Verschuere
Futures Hedging in Power Markets: Evidence from the European Energy Exchange (EEX) (close abstract)

We indicate how futures options can be hedged in realistic power markets. Most power exchanges maintain cascading rules when quoting power futures contracts. Consequently, the hedging of futures derivatives can be difficult, as the price of the underlying may remain hidden in the market for some time. In this paper, we propose a valuation method for futures options based on evidence collected from the European Energy Exchange.
 

Umut Cetin
Structure Equations with an Application to Finance (close abstract)

We'll give a brief overview of structure equations and Azema martingales with an application to default risk.
 

Johannes Leitner
Balayage monotonous risk measures (close abstract)

We consider coherent risk measures which are in addition monotonous with respect to taking conditional expectation.
 

Fabrice Baudoin
Some aspects of stochastic differential equations driven by loops (close abstract)

We study stochastic differential equations driven by semimartingales generating loops in the free Carnot group of step N and relate some properties of solutions to a certain Lie algebra.
 

Lutz v. Grafenstein (Attention: this talk starts at 11:00)
Feynman integral and related topics

Pavel Grigoriev (Attention: this talk starts at 11:00)
Polynomials with random coefficients (close abstract)

In the talk I give an overview of results concerning the distribution and expected value of maximum of random polynomials. This topic has some technical and ideological relations with Random Processes (supremum estimation and sample path continuity), Banach Space Geometry and Statistics (quantile estimates).
Besides the overview I mention my results in this area which in particular provide non-trivial lower estimates for norms which are weaker than the maximum one (i.e. the Marcinkiewicz norm).
 

Michel Verschuere (Attention: this talk starts at 11:00)
A regime switching model for power options (close abstract)

We revisit a valuation model for call options on power spot prices due to de Jong and Huisman. They have shown that both the strong mean reversion and price spikes observed for such prices can be captured in a regime switching approach. Based on this spot price model, closed option pricing formulas can be derived within the Black '76 context. However, such no-arbitrage based pricing is inappropriate, as electrical energy can not be economically stored. Therefore, power spot derivatives generally allow only for static hedging and their valuation becomes an actuarial issue rather than a financial one.
This is joint work with Lutz von Grafenstein (EU-Project TU Vienna, else TU Berlin).
 

Angelika Esser (Goethe University, Frankfurt, D) (14:30, Sem 107)
Modeling feedback effects with stochastic liquidity (close abstract)

We model the interactions between the trading activities of a large investor, the stock price, and the market liquidity. Our framework generalizes the model of Frey (2000) where liquidity is constant by introducing a stochastic liquidity factor. This innovation has two implications. First, we can analyse trading strategies for the large investor that are affected by a changing market depth. Second, the sensitivity of stock prices to the trading strategy of the large investor can vary due to changes in liquidity. Features of our model are demonstrated using Monte Carlo simulation for different scenarios. The flexibility of our framework is illustrated by an application that deals with the pricing of a liquidity derivative. The claim under consideration compensates a large investor who follows a stop-loss strategy for the liquidity risk that is associated with a stop-loss order. The derivative matures when the asset price falls below a stop-loss limit for the first time and then pays the price difference between the asset price immediately before and after the execution of the stop-loss order. The setup to price the liquidity derivative is calibrated for one example using real world limit order book data so that one gets an impression about the order of magnitude of the liquidity effect. (joint work with Burkart Mönch)
 

Juri Hinz (Eberhard-Karls Universität Tübingen, D) (9:30, Sem 107)
Modeling electricity auctions (close abstract)

The recent worldwide introduction of competition to electricity production and trading raises a number of interesting problems concerning optimal market design, risk estimation, and strategy optimization for power producers. We address the last problem, discussing an auction model which captures key features of real-time electricity trading. It turns out that, under certain conditions, the expected total payment to electricity producers is independent on particular auction type. This result is similar to the revenue equivalence theorem for classical auctions and could help to compare different electricity auction formats.
 

Christoph Hummel (Converium, CH) (Attention: this talk takes place at FH 3)
Tarifierung in der Kredit(rück-)versicherung
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Robert Tompkins
Unconditional disturbances: a new approach to asset pricing

Software-Firma eudaptics 16:30-18:00, FH 2
Der SOM-Kohonen-Algorithmus und seine Anwendung in der Finanzwirtschaft
Vortrag im Rahmen der Vorlesung Schadensversicherungsmathematik 2

Fabrice Baudoin
Stochastic control problems, viscosity solutions, and applications to finance (6)

Software-Firma SAS Austria 16:30-18:00, FH 2
Statistische Methoden und deren Umsetzung in der Sachversicherung
Vortrag im Rahmen der Vorlesung Schadensversicherungsmathematik 2

Michel Verschuere
Pricing Power Derivatives

Michael Schlögl (Wiener Städtische)
Die Optimierung einer Direkt-Mail-Kampagne - die praktische Anwendung von Segmentierungs- und Klassifikationsverfahren am Beispiel der Kraftfahrzeug-Versicherung (close abstract)

An einem simulierten Bestand werden die Möglichkeiten der Steigerung des Ertrages einer Mailing-Aktion anhand verschiedener Klassififkationsverfahren aufgezeigt.
Anhand des Beispiels werden die Anwendungsmöglichkeiten diskutiert und die Ergebnisse der Verfahren gegenübergestellt.
Unter Berücksichtigung der anfallenden Kosten wird die optimale Anzahl der Aussendungen ermittelt.
 

9:45-11:15, Sem 105
Martin Schaden (New York University)
The Distributions of Historic Stock Returns and Quantum Theory (close abstract)

The distributions of individual stock returns over time periods of less than 2 weeks observed by ref.[1] are accurately modelled by the square of an amplitude that has the form of a Cauchy distribution. On time scales of less than two weeks the only statistically relevant parameters of an individual stock are the mean and standard deviation of its distribution of returns. I argue that the observed shape stability of the distribution for time periods from 5 minutes to 2 weeks rules out an iid process and in general presents a problem for (most) stochastical models. I show that the distributions of the returns instead exhibit some properties one might expect from a quantum model. A very simple quantum Hamiltonian reproduces the observed short-term dynamics and, with a slight modification, semi-quantitatively gives the historic distribution of returns for time intervals up to 4 trading years.
[1] V Plerou, P.Gopikrishnan, L.N. Amaral, M. Meyer and H.E. Stanley, Phys.Rev. E60, 6519 (1999).
The talk is an extended version of the preprint available from http://xxx.lanl.gov/abs/physics/0205053
 

Umut Cetin (Cornell University)
Liquidity Risk and Arbitrage pricing Theory (close abstract)

Classical theories of financial markets assume an infinitely liquid market and that all traders are price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders, or for modeling transaction costs. We propose a new model that takes into account illiquidities, while extending the classical theory. In essence, we relax the standard assumption of a competitive market, where each trader can either buy or sell unlimited quantities of a stock at the market price. Our approach hypothesizes a stochastic supply curve for a securitys price as a function of trade size. This leads to some interesting mathematical issues, as well as natural restrictions on hedging strategies.
 

Laurent Nguyen (Université Paris 6)
Wiener-Hopf factorization for Lévy processes and some applications in mathematical finance (close abstract)

In an "exponential Lévy model", ie when an asset price is modelled as $S(t)=exp(X(t))$, where $X$ is a Levy process, the problem of pricing certain exotic options is studied; these options involve barrier, lookback, american and russian options. The Wiener-Hopf factorization of the Levy exponent of $X$ plays an important role in this study, as well as a path decomposition at the maximum similar to Williams' one for the Brownian motion.
 

Friedrich Hubalek
Stochastic control problems, viscosity solutions, and applications to finance (5)

Friedrich Hubalek
Stochastic control problems, viscosity solutions, and applications to finance (4)

Josef Teichmann
Stochastic control problems, viscosity solutions, and applications to finance (3)

Peter Grandits
Some remarks on asymptotic ruin probabilities and investment

Josef Teichmann
Stochastic control problems, viscosity solutions, and applications to finance (2)

Josef Teichmann
Generic evolutions of the term structure of interest rates (close abstract)

We provide a hypoellipticity result in the spirit of Paul Malliavin for the HJM-equation. The result can be interpreted as an argument for the necessity of finite dimensional realizations in interest rate theory.
 

Michel Verschuere
Stochastic control problems, viscosity solutions, and applications to finance (1)

Fabrice Baudoin, 15:00-16:30, FH HS 3
On the Markov property of radial motions on a Riemannian manifold (close abstract)

In this talk, we will study the radial parts of a Riemannian Brownian motion. It is well known that these radial parts are semimartingales in the underlying Brownian filtration. Our goal, here, is to study if they enjoy the Markov property or not. This Markov property is closely related to the action of the isometry group on the unit bundle. Precisely, we shall see that the only simply connected and compact manifolds for which these radial parts enjoy the Markov property (in DynkinŽs sense) are rank one symmetric spaces.
 

Josef Teichmann, 15:00-16:15,
Non-affine Term Structure Models

Walter Schachermayer; 17:15-18:00
Optimization of Dividend Payments

Andreas Eckner; 16:30-17:15
Pricing Derivatives of American and Game Type in Incomplete Markets (close abstract)

During the last years, various suggestions have been made how to price European-type contingent claims in incomplete markets. By contrast, there is only very little corresponding literature dealing with American options and in particular with Game options.
In the following, I describe two different pricing approaches for such contingent claims. Namely, utility maximization of terminal wealth and local utility maximization. The role of the arbitrage-free price in complete financial markets will now be played by the neutral derivative value. This is the unique price such that the speculators's optimal portfolio contains no contingent claim. In other words, this is the unique derivative price such that nobody can benefit from trading the contingent claim.
As we will see, American contingent claims can be treated as special cases of Game contingent claims. Moreover, all results simplify to the well known pricing formulas for contingent claims in the special case of a complete financial market.
 

Jacopo Zani; Banca IMI, Politecnico of Turin
Static Hedging of Barrier Options

Eva Strasser
On the Duality Theorem of Utility Maximization (close abstract)

The present paper deals with a version of the duality theorem of convex optimization. As a special case, we obtain a general version of the duality theorem of the problem of utility maximization in the context of mathematical finance. In particular, we are in a position to generalize results by Kramkov and Schachermayer (1999), Cvitanic, Schachermayer and Wang (2001) and Zitkovic (2002). In contrast to these results, the utility function under consideration satisfies only very weak regularity resp. growth conditions. Moreover, we do not assume that the domain of the problem of utility maximization is closed (in the context of mathematical finance, this would be equivalent to the existence of an equivalent martingale measure). In order to prove the main theorem, we use different arguments than Kramkov and Schachermayer (1999), Cvitanic, Schachermayer and Wang (2001) or Zitkovic (2002). However, we take on some important ideas of the original proofs by Kramkov and Schachermayer (1999).
 

our seminar on "Coherent Risk Measures" continues

Josef Teichmann
Cubature on Wiener Space, II (close abstract)

We present some recent results due to Terry Lyons and Nicoals Victoir on approximations of expected values on Wiener space. Given a parabolic PDE it is well known that the solution can be represented as an expected value on Wiener space. As in finite dimensional theory this integral is calculated by carefully choosing some footpoints and appropriate weights in order to approximate the value by a finite sum. We present the method and the algorithm.
 

our seminar on "Coherent Risk Measures" continues

Josef Teichmann
Cubature on Wiener Space, I (close abstract)

We present some recent results due to Terry Lyons and Nicoals Victoir on approximations of expected values on Wiener space. Given a parabolic PDE it is well known that the solution can be represented as an expected value on Wiener space. As in finite dimensional theory this integral is calculated by carefully choosing some footpoints and appropriate weights in order to approximate the value by a finite sum. We present the method and the algorithm.
 

Zoran Vondracek
Levy Processes and Pollaczek-Khintchin formula (close abstract)

We consider a generalized risk reserve process $ X(t) = ct-C(t)+Z(t)$, where $ C(t) $ is a subordinator, and $ Z(t) $ a perturbation. This is a L{\'e}vy process with no positive jumps. By using the fluctuation theory for L{\'e}vy processes, we derive the Pollaczek-Khintchin formula for the ruin probability.
 

Igor Melichercik
Multi Stage Bond Portfolio Optimization under Model Risk (close abstract)

A method of bond portfolio management will be presented. Our approach is based on multi-stage stochastic programming. We calculate optimal decisions for several models. The final decision is made after analysis of a stress-testing. The efficiency of our method is tested on historical data of USD, CHF and DEM. The performance is compared to official benchmarks.
 

our seminar on "Coherent Risk Measures" continues

our seminar on "Coherent Risk Measures" continues

Gottwald Kranebitter (KPMG) (Attention: this talk takes place at FH HS 6)
Unternehmensbewertung
Vortragsreihe aus Finanz- und Versicherungsmathematik

The talk takes place at
our seminar on "Coherent Risk Measures" starts

Cristian Popa
Relaxation with measure-valued functions in problems of Best Approximation (close abstract)

The space of probability measure-valued functions, also called Young measures, is endowed with a norm-like structure. This research takes a closer look at the space of $1$-integrable Young measures and in particular we are investigating the problem of best approximation of an ordinary function in a convex set of Young measures. The natural best approximation in function spaces singles out, from the family of best $L_1$-approximation of an integrable function in a convex set, the element which is the limit as $p$ converges to $1+$, of the unique best $L_p$-approximation of the function. The existing result from function spaces is extended to convex sets in spaces of integrable Young measures. Such spaces lack a standard affine structure and the convexity is considered via a limiting procedure. Consequently, the proof of the existence of a natural best approximation does not rely on tools like weak convergence, which are available in an ordinary function space. Rather, the interplay of compactness and convexity in the relaxed setting plays a major role.
 

Rainer Münz
Alterung in Europa: Auswirkungen auf Kapitalmarkt und soziale Sicherung,
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Josef Teichmann, 14:30, Hörsaal 9, Hauptgebäude (map)
Geometrie der Zinsen (Habilitationsvortrag) (close abstract)

Anhand einfacher Beispiele werden geometrische Fragestellungen in der stochastischen Analysis eingefuehrt. Die endlichdimensionale Loesung wird dann geeignet auf unendlichdimensionale Problemstellungen verallgemeinert. Als Anwendung wird ein aktuelles Problem der Zinstheorie geloest, naemlich die Beschreibung aller endlichdimensionalen Realisierungen der HJM-Gleichung.
 

Christoph Kühn
Zur Bewertung von Amerikanischen Optionen und Spieloptionen in unvollständigen Märkten (close abstract)

In den letzten Jahren wurden viele Vorschläge gemacht, wie Derivate europäischen Typs in unvollständigen Finanzmärkten bewertet werden können. Im Gegensatz dazu gibt es nur wenige Ansätze für die Bewertung Amerikanischer Optionen. Daher analysieren wir Amerikanische Optionen und sog. "Spieloptionen" in einem allgemeinen "Semimartingal-Model". Spieloptionen verallgemeinern Amerikanische Optionen, indem sie dem Verkäufer die Möglichkeit einräumen, die Option, solange sie noch nicht vom Käufer ausgeübt worden ist, gegen eine Strafgebühr zurückzukaufen. In dem Vortrag wird auf den "neutralen Derivatebewertungsansatz" und das Konzept der "nutzenbasierten Indifferenz-Bewertung" eingegangen.
 

Halbtages-Seminar (Attention: different time and place)
Dynamische Finanzanalyse und Asset-Liability-Management
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Thorsten Schmidt, 17:00-18:00
Credit Risk (close abstract)

Die Literatur im Bereich Credit Risk unterscheidet zwei Modellansätze zur Bewertung von Ausfallrisiken. Eine kurze Einführung in die verschiedenen Modelle beleuchtet Vor- und Nachteile der Structural bzw. Intensity Based Models.
Im zweiten Teil stellen wir ein neues Credit Risk Modell vor, was auf Gaußschen Random Fields basiert. Neben Bedingungen für die Arbitragefreiheit des Modells erhalten wir explizite Price- und Hedgeformeln für Optionen.
 

Peter Bank, 16:00-17:00
Hedging and Portfolio Optimization in Illiquid Financial Markets (close abstract)

We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter dependent semimartingales, and its mathematical analysis relies on the non-linear integration theory of such semimartingale families. The Ito-Wentzell formula is used to prove absence of arbitrage for the large investor, and using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.
 

Alexander Cherny
On the Strong and Weak Solutions of Stochastic Differential Equations Governing Bessel Processes (close abstract)

We study the stochastic differential equation
$$
dX_t=\frac{\delta-1}{2 X_t} I(X_t\ne0)\,dt+dB_t,\quad X_0=x.\eqno(*)
$$
This is the equation for the $\delta$-dimensional Bessel process started at $x\ge0$. Here, $\delta>1$. We prove the following statements.

The $\delta$-dimensional ($\delta>1$) Bessel process is the unique (with fixed $x$ and $B$) {\it nonnegative} solution of $(*)$. Moreover, it is a strong solution.

If $\delta\ge2$ and $x>0$, then the pathwise uniqueness holds for $(*)$.

If $1<\delta<2$ or $x=0$, then

a) there exist other strong solutions (with the same $x$ and $B$);

b) there exist weak solutions;

c) the uniqueness in law does not hold for $(*)$.


 

Paolo Guasoni
Optimal Investment with Transaction Costs and without Semimartingales (close abstract)

We consider a general class of optimization problems in financial markets with incomplete information and transaction costs. Under a no-arbitrage condition strictly weaker than the existence of a martingale measure, and when asset prices are quasi left-continuous processes, we show the existence of optimal strategies.

Applications include maximization of expected utility, minimization of coherent risk measures, and hedging of contingent claims.
 

Fabrice Baudoin
Conditioned Stochastic Differential Equations - Applications to Finance (close abstract)

(1) We generalize the notion of Brownian bridge. More precisely, we study a standard Brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations that we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general presentation several examples are studied: the conditioning of a standard Brownian motion (and more generally of a Markov diffusion) by its value at a given date, and the conditioning of a standard Brownian motion by its first hitting time of a given level.
(2) As an application, we introduce the notion of weak information on a complete or incomplete market, and we give a "quantitative" value to this weak information.
(3) As the end of the talk, we will go one step further by considering a flow of information: as the price process is revealed, the weak anticipation is updated.
 

Alfred Müller (Attention: this talk starts at 16:00 and takes place at FH HS 6)
Abhängigkeitsordnungen und ihre Anwendungen in der Versicherungsmathematik (close abstract)

Viele stochastische Modelle insbesondere in der versicherungs- und finanzmathematischen Literatur basieren auf der unrealistischen Annahme, dass Komponenten der Modelle (wie z.B. Risiken zu verschiedenen Zeitpunkten, Risiken verschiedener Produkte oder verschiedener Kunden etc.) stochastisch unabhängig sind. Es ist aber bekannt, dass diese Annahme in der Realität nicht zutrifft. Deshalb wird in jüngerer Zeit vermehrt versucht, Abhängigkeiten zu modellieren, und deren Auswirkungen zu studieren. In diesem Vortrag werden Ordnungsrelationen für Zufallsvektoren vorgestellt, welche die Stärke der Abhängigkeit zwischen den Komponenten vergleichen. Insbesondere wird auf die sogenannte supermodulare und die richtungskonvexe Ordnung eingegangen. Diese werden dann benützt, um den Einfluss von Abhängigkeiten auf Kenngrössen einiger stochastischer Modelle aus der Finanz- und Versicherungsmathematik zu studieren.
(Alfred Müller)
 

Peter Koenig (Attention: this talk takes place at FH HS 6)
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Michel Verschuere
TBA

Eva Strasser
Several Remarks on Arbitrage-Free Markets (close abstract)

Let $S=(1,S^1,...,S^d)$ be a continuous semimartingale. We prove that $S$ satisfies the NA-property with respect to admissible integrands if and only if there exists an absolutely continuous local martingale measure $Q^\sigma$ for the market starting at $\sigma$, for every stopping time $\sigma$. A general version of the necessity part is already known from Delbaen and Schachermayer (1995).
As supplementary results we obtain characterizations of weaker notions of the NA-property.
 

Fred Espen Benth (Attention: this talk starts at 16:00)
Merton's portfolio optimization problem and non-Gaussian stochastic volatility (close abstract)

(joint work with Kenneth H. Karlsen, (University of Bergen), and Kristin Reikvam (KLP) )

We provide extend the classical Merton portfolio optimization problem to the case where the risky asset dynamics has a non-Gaussian stochastic volatility. In particular, we consider the stochastic asset dynamics introduced by Barndorff-Nielsen and Shephard (2001). An explicit investment strategy is calculated, and a Feynman-Kac formula for the value function is derived. We finally discuss a numerical example and some extensions to option pricing in incomplete markets.
 

Friedrich Hubalek
Three notes from recent work (close abstract)

A counterexample related to affine processes

On the simulation from moderately tractable Levy processes

Some special functions arising in the implementation of stochastic volatility models
 

Georg Pflug Attention: this talk takes place at FH HS 6
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Damir Filipovic
9:30, HS 18 Czuber
Stochastische Zinsmodelle (close abstract)

Dieser Vortrag erläutert das Zusammenspiel zwischen Schätzmethoden und stochastischen Modellen für die Zinsstrukturkurve.
Einerseits sind parametrische Verfahren zur Schätzung der Zinsstrukturkurve wie diejenigen von Nelson und Siegel (1987) und Svensson (1994) weitverbreitet. Es handelt sich dabei um parametrisierte Familien von Kurven, welche durch optimale Wahl eines endlich dimensionalen Parameters bestmöglich an die gegebenen Marktdaten (Anleihenpreise, Swaps, Terminzinsprodukte, Optionen auf Anleihen, usw.) angepasst werden.
Andererseits wird die arbitragefreie, stochastische zeitliche Entwicklung der Zinsstrukturkurve in kanonischer Weise durch einen hilbertraumwertigen Markovprozess beschrieben. Alle geläufigen Zinsmodelle sind von dieser Form.
Für praktische Zwecke ist es daher wichtig zu bestimmen, welche dieser stochastischen Zinsmodelle mit den obigen Schätzverfahren verträglich sind, das heisst ebensolche parametrisierte Kurven produzieren. Die Frage kann allgemeiner gestellt werden: Welche stochastischen Zinsmodelle erlauben eine endlich dimensionale Realisierung und sind somit überhaupt sinnvoll kalibrierbar? Die Antwort fällt erstaunlich klar aus: Es sind dies nur die affinen Zinsstrukturmodelle.
Zum Schluss wird daher ein Charakterisierungsresultat für allgemeine affine Modelle präsentiert, welche ihrerseits eine Vielfalt von Anwendungen versprechen.
 

Freddy Delbaen
Monotone on-line selections in Poisson arrival processes (close abstract)

(joint work with Th. Bruss, ULB Brussels)

The problem is the following: there is an arrival processs modelled by a Poisson process (with arrival rate 1). At each arrival time there is (i.i.d. and independent from the arrival process) a random variable that is uniformly distributed [0,1]. At each time you can either "accept" the outcome of this random variable or reject it. The rules are that the ones you accepted should form an increasing sequence. Given an horizon (t), what is the optimal expected number v(t) of accepted outcomes and what is the optimal strategy? This leads to a nonlinear integral equation (called Gnedin's equation).

v'(t) = \int_0^1 (1 + v(x t) - v(t) )^+ dx with v(0) =0.

The asymptotics of v(t) and v'(t) are known and there are sharp estimates such as

\sqrt(2t) \ge v(t) \ge \sqrt(2t) - const * log(t+1). (The constant is moderate).

Previous work on this problem only gave estimates from above and from below with extra terms of the order t^{1/4}. We also can prove central limit theorems for the counting process as well as for the maximum level of accepted outcomes. Our methods also allow to give an existence and uniqueness proof for the solution of the integral equation.
 

Rama Cont
Methods for model calibration

our seminar on "Optima and Equilibria" continues

Michael Kirch
No-arbitrage bounds of option prices if asset prices are piecewise constant (close abstract)

We examine the interval of arbitrage free prices for an European option with convex payoff function on an asset with piecewise  constant price process. We first establish trivial, model-independent bounds on the price of the option. These allow either the seller or the buyer of the option to make a riskless profit. We then show that the interval of arbitrage free prices coincides with the open interval spanned by these bounds. We also derive the fundamental theorem of asset pricing for the continuous time model by means of the fundamental theorem of asset pricing for  one-period models and establish simple conditions for no-arbitrage.

This study can be seen as complementary to the analysis carried out by Eberlein and Jacod (1997), where similar results where achieved for a purely discontinuous price process which has jumps of arbitrarily large size on any non void time interval.

Our results illustrate the need for alternative hedging strategies that require less initial capital than the superhedge price. If time permits, we will sketch how one can derive the efficient hedging strategy for an European option in this model and discuss issues arising from model-uncertainty.
 

Paul Embrechts Attention: this talk takes place at FH HS 6
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Uwe Schmock (Universität Zürich)
15:00, Freihaus HS 7
Modellierung abhängiger Kreditrisiken

Hans-Jochen Bartels (Universität Mannheim)
10:30, Freihaus HS 7
Symmetrierelationen für ein inverses Problem der Finanzmathematik

no seminar, but see at the IHS

Freddy Delbaen
On the Structure of the Set of Risk Neutral Measures

Ludger Rüschendorf
11:15-12:30, Seminarraum 107
Adaptives Schätzen mit Schätzern vom neuronalen Netztyp (close abstract)

We obtain consistency results and determine convergence rates for neural nets type estimators. In detail we consider the estimation of the log-hazard function in random censoring models with covariates. Our results are based on a general approach to sieved maximum likelihood estimators (or minimum contrast estimators) including an adaptive version of the estimators based on the method of structural risk estimation. A related approach was developed recently in Birge Massart(1998) and Barron Birge Massart(1999). In comparison we obtain upper bounds for the estimation error involving more simple covering numbers. We discuss two types of applications of the general results. For smoothness classes we establish an adaptive version of the tensor product spline estimator as introduced in Kooperberg Stone Truong(1995a). The minimax optimal rate of convergence is not achieved for the standard sigmoidal neural net estimator but is attained approximatively for some other activation functions as e.g. for the threshold function. Assuming the existence of a certain integral representation of the log-hazard function which is related to some smoothness conditions, we obtain improved convergence rates for net sieves type estimators as neural nets, radial basis function nets and wavelet nets. Similar convergence rate results have been established before for regression estimation in Barron(1993) and for density estimation in Modha Masry(1996). Our improvement of the convergence rate is based on an improved approximation result for functions of this type by finite net classes.
 

Irina Penner
On No Arbitrage Criteria for Financial Markets with Proportional Transaction Costs in Discrete Time (close abstract)

For a multi-asset discrete-time model of a financial market with proportional transaction costs several no-arbitrage criteria have been introduced and studied by Kabanov, Rasonyi, Stricker and, more recently, by Schachermayer. In this talk we will discuss the so-called weak and strict no arbitrage conditions, introduced by Kabanov and Stricker, and the connection of these criteria with the concept of robust no arbitrage, introduced by Schachermayer. Using Kabanov's approach for modeling a bid ask spread by a price process and a matrix of transaction costs coefficients we will show, that the strict no arbitrage condition implies the robust no arbitrage under some restrictions on the matrix of transaction costs.
 

Nicole Baeuerle (Universitaet Ulm)
15:30, Freihaus HS 8 (Noebauer-Hoersaal)
Stochastische Steuerung in der Versicherungsmathematik (close abstract)

Das Problem der Bestimmung optimaler Dividendenaus- schüttungs- und Rückversicherungsstrategien, das in Teilen schon auf de Finetti (1957) zurückgeht, wurde in letzter Zeit wieder intensiv untersucht. Da die ursprüngliche Formulierung auf die optimale Steuerung eines stückweise deterministischen Markov Prozesses führt - was sehr schwierig ist - standen in letzter Zeit Diffusionsmodelle im Vordergrund. In dem Vortrag wird auf beide Formulierungen eingegangen und ein Zusammenhang zwischen den Optimierungsproblemen hergestellt.
 

Jeffrey Collamore (ETH-Zuerich)
13:15, Freihaus HS 8 (Noebauer-Hoersaal)
Extremal Behavior of Multidimensional Risk Processes (close abstract)

In the classical ruin problem of collective risk theory, an insurance company gains capital from premiums income and loses capital as a result of claims; one then studies the probability that the company's total capital ever falls below zero, i.e., P{S(t) < -m, for some t}, where S(t) is a positive-drift Levy process and m is the company's initial capital.

In this talk I will discuss various generalizations of this problem to higher dimensional settings. The first of these can be described as follows: Let S(1),S(2),... be a sequence of random vectors, corresponding e.g. to several capital factors, and consider the probability that this sequence ever reaches some "forbidden region" in d-dimensional Euclidean space. It will be shown that, under quite general assumptions,

(*) (1/m) log P{S(n) ever hits mA} ~ -I(A)

for an appropriate "rate function" I(A). Some refinements, describing e.g. the asymptotic distribution of the first passage time, will also be given.

A second generalization which will be discussed is the case where the increments of S(1),S(2),... are governed by a system of random recurrence equations. Such recurrence equations are of considerable

applied interest and arise, among other places, in the study of GARCH financial time series models and insurance models with stochastic returns on the surplus capital. It will be shown that an asymptotic estimate very similar to (*) can also be developed in this setting.
 

Alessandro Sbuelz
Asset pricing with time-varying pessimism (close abstract)

We present a flexible analytical framework that incorporates the equilibrium impact of state dependent investors' pessimism in continuous time intertemporal asset pricing. State dependent pessimism is modelled as a time varying confidence in some reference belief on equity returns dynamics and induces conservative optimal policies precisely in states where investors' confidence is low. Due to the complexity of the implied optimization problems we adopt a perturbative approach to compute first order approximations for the relevant equilibrium quantities. We find that to first order our parameterization of pessimism does not affect expected returns on equity and their variances and covariances with the opportunity set process. Pessimism rather determines a pure asset substitution, from which lower equilibrium interest rates and higher equity premia are generated through first order risk aversion effects. In two illustrative explicit examples we show that parameterizing pessimism as a function of expected aggregate consumption growth can produce time varying pessimistic equity premia in models with otherwise constant premia. On the other hand, a parameterization depending on the conditional variance of dividend growth produces a time varying pessimistic equity premium that is proportional to dividend growth volatility in models where otherwise premia are proportional to conditional variances.
 

Josef Teichmann
Applications of Malliavin Calculus to Mathematical Finance, part II (close abstract)

The talk will be based upon the paper by Eric Fournie et al., Finance and Stochastics 3, 391 - 412 (1999).
 

our seminar on "Optima and Equilibria" continues

Josef Teichmann
Applications of Malliavin Calculus to Mathematical Finance (close abstract)

The talk will be based upon the paper by Eric Fournie et al., Finance and Stochastics 3, 391 - 412 (1999).
 

our seminar on "Optima and Equilibria" continues

Uli Haböck
Arbitrage-free asset pricing with proportional transaction costs, a paper of Zhang, Xu and Deng

our seminar on "Optima and Equilibria" continues

Franz Liebmann
Risikobereitschaft von Versicherungsunternehmen (close abstract)

Ausgehend von der Ungleichung von Cramèr lässt sich eine obere Schranke für die Risikobereitschaft von Versicherungsunternehmen angeben. Die Berechnung der oberen Schranke kann mit Hilfe von Schätzwerten für die Erwartungswerte und die Varianzen der Ergebnisse (Prämieneinnahmen minus Versicherungsleistungen) der vergangenen Versicherungsjahre durchgeführt werden. Dabei wird angenommen, dass das Portefeuille die recht allgemeinen Voraussetzungen der Ungleichung von Cramèr erfüllt.
Anhand der Ergebnisse der Jahre 1987 bis 1996 wurde die Risikobereitschaft für die vierzehn größten österreichischen Schaden- / Unfallversicherer ermittelt. Die Risikoaversion (Kehrwert der Risikobereitschaft) wurde der Eigenkapitalausstattung gegenübergestellt. Dabei zeigten sich signifikante Abweichungen. Die Beurteilung der Versicherungsunternehmen anhand weiterer Kennzahlen zeigt, dass die Risikoaversion die Sicherheit der untersuchten Versicherungsunternehmen besser beschreibt, als die Eigenkapitalausstattung auf Basis der derzeitigen Solvenzbestimmungen.
Es wäre zu überlegen, die derzeitigen Solvabilitätsvorschriften der EU-Richtlinien durch eine Bestimmung über eine maximale Risikobereitschaft zu ergänzen. Eine sehr knappe oder gar unzureichende Bildung von Rückstellungen hat selbstverständlich einen viel größeren Einfluss auf die Liquidität eines Versicherungsunternehmens, als eine Erhöhung des Eigenkapitals, und kann durch die hier vorgeschlagene Ergänzung nicht verhindert oder gar ersetzt werden. Immerhin würden durch diese Ergänzung jene Versicherungsunternehmen erfasst werden, deren Portefeuilles eine hohe Risikobereitschaft erkennen lassen.
Durch die Ergänzung soll die Risikobereitschaft beschränkt werden. Die Gefahr, dass die Risikobereitschaft durch den beschriebenen Ansatz zu niedrig geschätzt wird, ist meines Erachtens gering. Eine Unterschätzung könnte auftreten, wenn die Voraussetzungen für die Gültigkeit der Ungleichung von Cramèr nicht erfüllt sind. Wegen der sehr allgemeinen Voraussetzungen, welche für die Gültigkeit der Ungleichung von Cramèr erforderlich sind, kann angenommen werden, dass die Risikobereitschaft in den meisten Fällen eher geringer sein wird, als sie durch diesen Ansatz geschätzt wird. Kann ein Versicherungsunternehmen aufgrund der Kenntnis seines Portefeuilles nachweisen, dass seine Risikobereitschaft deutlich unter der, auf Grund der Ungleichung von Cramèr berechneten Obergrenze liegt, müsste es dem Versicherungsunternehmen gestattet sein, eine begründete, genauere Abschätzung zu verwenden.
 

Leszek Krawczyk
to be announced

Patrick Cheridito
Fractional Ornstein-Uhlenbeck processes

Patrick Cheridito
10:00, Besprechungszimmer, 6th floor, green area
Introduction to fractional Brownian motion

our seminar on "Optima and Equilibria" continues

Hans Bühlmann Attention: this talk takes place at FH HS 8
Vortragsreihe aus Finanz- und Versicherungsmathematik, details

Michael Kirch
Preference Free Restrictions on Option Prices in Equilibrium

our seminar on "Optima and Equilibria" continues

Ioannis Karatzas, Department of Mathematics and Statistics, Columbia University
this talk starts at 15:30
Optimal Portfolio/Consumption under Habit-Formation

Marcel Straka
Indifference Prices and Related Measures (part II) (close abstract)

The talk will be about the paper Indifference Prices and Related Measures by M.Musiela and T.Zariphopoulou.

The traditional approach towards derivative pricing consists of dynamically replicating a future liability by trading the assets on which that liability is written. However, the assumption that one can trade the assets is often rather restrictive. In some cases, say of options on commodities or funds, one can at best trade another correlated asset. In others, as in the case of basket options, even when one can trade the basket components, for effciency reasons one may still prefer to use a correlated index for pricing and hedging. Due to the departure from the traditional assumptions of valuation by replication and no arbitrage considerations, one needs to review the pricing and hedging methodologies to accommodate the above situations. Utility-based approach is developed herein for the specification of indifference price of claims written on non-traded assets. The pricing mechanism is based upon the parity between the maximal utilities, with and without employing the derivative. The residual amount gained from granting the option, which renders the investor impartial towards these two scenarios, is called the indifference price. Under exponential risk preferences such a price can be calculated by a nonlinear transformation of a solution to a linear parabolic equation. The transformation is independent of the risk preferences and only depends on the correlation between the traded and the non-traded risky assets. The equation is associated with a diffusion process whose dynamics are in turn identified by solving a relevant Hamilton-Jacobi-Bellman equation. The new diffusion turns out to be a drift-modified diffusion of the original one modelling the level of the non-traded asset. The drift modification corresponds to a new measure, referred to as the indifference measure, which depends on the correlation and the Sharpe ratio of the traded risky asset.
 

Eva Strasser Attention: 16:00 - 16:45
Working Paper: On A Question Raised By Schachermayer (close abstract)

The present paper deals with necessary and sufficient conditions for the supermartingale property of a stochastic integral with respect to a local martingale. Ansel and Stricker give a familiar answer to this question. Recently, Schachermayer as well as Kabanov and Stricker have dealt with this problem, too. The main result of the present paper is a counterexample showing that the conditions of the result by Schachermayer cannot be weakened without imposing additional conditions. This counterexample can also be applied to the version by Kabanov and Stricker. Moreover, we present some results simplifying the known proofs and improving the conditions of the lemmas by Schachermayer and by Kabanov and Stricker. By means of this improvement we obtain that the existence of an equivalent local martingale measure yields a much broader class of arbitrage-free wealth-processes than those which are considered in the usual theory.
 

Marcel Straka
Indifference Prices and Related Measures (close abstract)

The talk will be about the paper Indifference Prices and Related Measures by M.Musiela and T.Zariphopoulou.

The traditional approach towards derivative pricing consists of dynamically replicating a future liability by trading the assets on which that liability is written. However, the assumption that one can trade the assets is often rather restrictive. In some cases, say of options on commodities or funds, one can at best trade another correlated asset. In others, as in the case of basket options, even when one can trade the basket components, for effciency reasons one may still prefer to use a correlated index for pricing and hedging. Due to the departure from the traditional assumptions of valuation by replication and no arbitrage considerations, one needs to review the pricing and hedging methodologies to accommodate the above situations. Utility-based approach is developed herein for the specification of indifference price of claims written on non-traded assets. The pricing mechanism is based upon the parity between the maximal utilities, with and without employing the derivative. The residual amount gained from granting the option, which renders the investor impartial towards these two scenarios, is called the indifference price. Under exponential risk preferences such a price can be calculated by a nonlinear transformation of a solution to a linear parabolic equation. The transformation is independent of the risk preferences and only depends on the correlation between the traded and the non-traded risky assets. The equation is associated with a diffusion process whose dynamics are in turn identified by solving a relevant Hamilton-Jacobi-Bellman equation. The new diffusion turns out to be a drift-modified diffusion of the original one modelling the level of the non-traded asset. The drift modification corresponds to a new measure, referred to as the indifference measure, which depends on the correlation and the Sharpe ratio of the traded risky asset.
 

our seminar on "Optima and Equilibria" continues

Rainer Münz
Was leisten Bevölkerungsprognosen? (close abstract)

Bevölkerungsprognosen und Projektionen erfüllen in der Demographie zwei ganz unterschiedliche Zwecke: zum einen sollen sie Aufschluss über erwartbare Entwicklungen geben. Dann sprechen wir von Prognosen im eigentlichen Sinn. Zum anderen verdeutlichen Modellrechnungen interne Zusammenhnge zwischen einzelnen Parametern: insbesondere die strkere oder schwchere Abhngigkeit der in der Projektion analysierten Populationsdynamik von den getroffenen Annahmen zu Fertilitt, Mortalität und (ggf.) Migration. Dies soll anhand zweier aktueller Bevölkerungsprognosen für die Schweiz - der offiziellen des Bundesamts für Statistik (Neuchâtel) und einer eigenen vom Oktober 2001 -demonstriert werden. Zugleich geht es darum, die Grenzen der in der Demographie üblicherweise verwendeten Ein-Generationen-Modelle aufzuzeigen und Alternativen zu diskutieren. Bei entsprechendem Interesse an der Thematik wird in einem Folgeseminar über die Entwicklung eines Mehr-Generationen-Modells und über praktische Applikationsmöglichkeiten berichtet.
 

Sasha Gorbulsky
Some entropy type invariants of decreasig sequences of measurable partitions (close abstract)

I'll talk about the old defenition of entropy of decreasing sequences of measurable partitions. - I'll try to give all the definitions. Some examples of nonstandard sequences with positive and zero entropy.
A new entropy-type invariant - "scaling entropy" - some properties and relations with the old notion of entropy. The scaling entropy of one nonstandard sequence of partitions.
 

Josef Teichmann
Filtering Problems from the geometric point of view (close abstract)

It is possible to relate prices of several derivatives to certain convex bodies. This paves the way to relate many financial problems to the machinery of instruments provided by convex geometry. Furthermore, geometric properties can be translated into economic statements and vice versa. For instance, considering asset prices at maturity, the European put-call parity can be explained by point symmetry while the univariate duality-principle in option pricing corresponds to a reflection, explaining classical European put-call symmetry by line-symmetry. This motivates natural extensions of put-call symmetry in the multiasset setting. Interestingly, the well-known exchangeability of random vectors has a similar geometric interpretation and can be related to put-call symmetry with the help of a reduction of dimensionality by applying multivariate duality-principle techniques. In order to extend the range of applications, it is possible to transform some multivariate asymmetric distributions (bodies) to symmetric ones. A particular attention is devoted to the case of prices driven by Lévy processes. Both phenomena, multivariate put-call symmetry and exchangeability, can be applied for creating semi-static hedges of certain multiasset barrier options. If there is enough time, some other relations between financial questions and geometric phenomena will be discussed.
 

our seminar on "Optima and Equilibria" continues

Johanna Gaier
Asymptotic Ruin Probability and Optimal Investment for an Insurance Company with Small Claims (close abstract)

The talk will be about a joint paper with Peter Grandits and Walter Schachermayer. We study the infinite time ruin probability in the classical Cramér-Lundberg model with finite exponential moments, where the company is also allowed to invest their money in some stock market, modeled by geometric Brownian Motion. We are able to obtain an exact analogue of the classical estimate for the ruin probability without investment, i.e. an exponential inequality. The exponent obtained is larger than the one obtained without investment, and thus one gets a smaller bound on the ruin probability. Further it is shown that a certain constant investment strategy is asymptotically optimal.
 

our seminar on "Optima and Equilibria" continues

Walter Schachermayer
The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time (close abstract)

We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's approach to foreign exchange markets under transaction costs. The financial market is modelled by a $d \times d$ matrix-valued stochastic process $(\Sigma_t)_{t=0}^T$ specifying the mutual bid and ask prices between $d$ assets.
We introduce the notion of ''robust no arbitrage'', which is a version of the no arbitrage concept, robust with respect to small changes of the bid ask spreads of $(\Sigma_t)_{t=0}^T$. Dually, we interpret a concept used by Kabanov and his co-authors as ``strictly consistent price systems''. We show that this concept extends the notion of equivalent martingale measures, playing a well-known role in the frictionless case, to the present setting of bid-ask processes $(\Sigma_t)_{t=0}^T$.
The main theorem states that the bid-ask process $(\Sigma_t)_{t=0}^T$ satisfies the robust no arbitrage condition iff it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Dalang-Morton-Willinger to the present setting, and also generalizes previous results obtained by Kabanov, Rasonyi and Stricker.
An example of a $5 \times 5$-dimensional process $(\Sigma_t)_{t=0}^2$ shows that, in this theorem, the robust no arbitrage condition cannot be replaced by the so-called strict no arbitrage condition, thus answering negatively a question raised by Kabanov, Rasonyi and Stricker.
 

our seminar on "Optima and Equilibria" continues

Patrick Cheridito
Sensitivity of the Black-Scholes option price to the local path behaviour of the stochastic process modelling the underlying asset (close abstract)

We show that a change of the local behaviour of the stock price in the Black-Scholes model can lead to totally different option prices.
 

Christopher Summer
Risk Averse Asymptotics and the Optional Decomposition (close abstract)

The talk will be about a joint paper with Peter Grandits. We consider the problem of maximizing expected utility under the exponential utility function when the agent becomes increasingly risk averse. The limiting strategy will be constructed and we will characterize the limiting outcome as a maximal element with respect to a total ordering. This outcome will also be shown to correspond to the optional decomposition and the minimal hedging strategy described in Kramkov, "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets". The results are shown for two different settings: either for a complete underlying market or for a general market, but finite probability space.
 

our seminar on "Optima and Equilibria" continues

Hansjörg Albrecher, Department of Mathematics, Graz University of Technology
this talk starts at 17:00 at the usual place
On some generalizations of the classical ruin model in risk theory (close abstract)

The classical model in collective risk theory for the development of the free reserve of an insurance portfolio is characterized by a Poisson claim number process, independent and identically distributed claims and a constant premium density. Several generalizations of this model are considered. In a ruin model allowing for a constant force of inflation and interest on the free reserve, we investigate when it is suitable to represent the finite-time survival probability as a gamma series and derive some exact analytical solutions for exponentially distributed claim sizes. In a model with dividend payments according to a non-linear dividend barrier strategy, integro-differential equations for the survival probability and the expected discounted dividend payments are derived and, using integral operators, efficient number-theoretic solution methods are developed. Moreover we investigate the behavior of the Lundberg exponent when dependence structures among consecutive claims are considered.
 

Kerry Back, John M. Olin School of Business, Washington University in St. Louis
Information in Securities Markets: Kyle meets Glosten and Milgrom (close abstract)

We study a model of informed trading in which trades arrive sequentially, uninformed trades arriving as a Poisson process. We characterize an equilibrium in which the single informed trader plays a mixed strategy - a point process with stochastic intensity. In this equilibrium, informed and uninformed trades arrive probabilistically, as they are assumed to do in Glosten-Milgrom models. We study a sequence of such markets in which uninformed trades become smaller and arrive more frequently, approximating a Brownian motion. We show that if the equilibria converge, then their limit is the equilibrium of a Kyle-type continuous auction model.
 

our seminar on "Optima and Equilibria" continues

Robert Tompkins ATTENTION: this talk starts at 17:30
The relation between implied and realised probability density functions (close abstract)

By Iliana Anagnou, Mascia Bedendo, Stewart Hodges and Robert Tompkins
A number of financial regulators [see Neuhaus (1995), Bahra (1996, 1997), McManus (1999) and Shiratsuka (2001)] have suggested that risk neutral densities (RND) associated with options markets could provide useful indicators of future market turbulence. Critical to this assumption is that such RNDs should provide an unbiased forecast of realised probability density functions. To date, this assumption has not been fully examined.
In this research, we test the ability of RNDs for options on the S&P 500 and the British Pound / US Dollar to predict future probability densities. We consider three approaches to estimate the RNDs, which are consistent with approaches proposed and used by financial regulators. We also provide a number of new testing procedures to assess the efficiency and unbiasness of the forecasts. These tests provide more power than the usual Komolgorov/Smirnov tests.
Using non-overlapping quarterly data from the mid 1980s to 2000, we find that we can reject the hypothesis that the RNDs for both the S&P 500 and British Pounds are unbiased forecasts. Even with a limited number of observations, the tests are powerful enough to allow rejection. These results are consistent with Weinberg (2001) and are more robust as this work relied upon the use of overlapping data.
These results tend to support the conclusions of Shiratsuka (2001), that RNDs should not be used by financial regulators as financial indicators, and that such use could prove counterproductive; actually increasing future market turbulence rather than alleviating it.
 

our seminar on "Optima and Equilibria" starts

Friedrich Hubalek
Long forward rates never fall - A general proof of the Dybvig-Ingersoll-Ross Theorem (close abstract)

A general proof of the Dybvig-Ingersoll-Ross Theorem on the monotonicity of long forward rates is given by a little lemma on L^p-spaces. Based on joint work with Irene Klein and Josef Teichmann.
 

Alexei Filinkov, Department of Pure Mathematics, University of Adelaide
Interest Rate Theory and White Noise Calculus

Peter Grandits
Ruin Probability in the Presence of Regularly Varying Tails and Optimal Investment

Irene Klein, Josef Teichmann
Do long forward rates never fall? (close abstract)

The (small) note is based on an article by Dybvig, Ingersoll and Ross (1996), where the authors claim, that long zero coupon and forward rates can never fall in an arbitrage free interest rate model. They provide a strategy as argument for this assertion. We believe that there are some corrections to be made (an additional assumption, some limitation assumptions), such that the argument goes through. Furthermore we provide a martingale approach to the problem under these assumptions.