Vienna-Zurich Symposium for young researchers in Financial Mathematics and related fields (ViZuS 2019)

The first Vienna-Zurich Symposium for young researchers in Financial Mathematics and related fields (ViZuS 2019) will be held from November 27-29, 2019, at the Freihaus building of TU Wien.

The symposium will provide a platform for young researchers to present and discuss their current work - all participants are invited to give a talk of about 25 minutes or to present a poster. It will be a great opportunity to meet new people working in a variety of fields in Financial Mathematics as well as to tighten existing contacts.

Traditionally there has been a fruitful academic exchange between scientists in Zurich and Vienna - this symposium will intensify future research cooperation especially of the "next generation".

The symposium will consist of talks from Wednesday afternoon (starting 15:00) to Friday evening (18:30). Additionally, there will be a social event on Friday evening as well as joint sightseeing on the weekend.


 

 


Speakers

Special Guest / Keynote Speaker

Invited Speakers from Switzerland

Speakers from Austria


 

 


Abstracts

Special Guest / Keynote Speaker

Walter Schachermayer (University of Vienna)
"Stochastic Portfolio Theory"
We give a survey of recent results.

Speakers

Andrew Allan (ETH Zurich)
"Parameter Uncertainty in Stochastic Filtering"
We consider the problem of filtering - that is, estimating the current state of a stochastic 'signal' process from noisy observations - under uncertainty of both the dynamics of the signal and of its relationship with our observations. We take a nonlinear expectations approach, which leads naturally to a pathwise stochastic optimal control problem, the solution of which provides a new way of 'learning' unknown parameter values dynamically through time.

Aleksandar Arandjelovic (FAM @ TU Wien)
"Approximations in Weighted Hölder Spaces"
We revisit some classical approximation results in Hölder spaces and extend them, allowing for a more generalized setting. If time permits, we will also discuss approximations of càdlàg paths in the space of tempered distributions, as well as applications to large deviation theory.

Lukas Fertl (TU Wien)
"Conditional Variance Estimator for Linear Dimension Reduction"
In this talk I will introduce a new way of estimating the dimension reduction matrix B in the classical sufficient dimension reduction modell y=f(B'x)+ ε with additive errors ε. The idea is based on considering the variance of y conditioned on x beeing in the span of a directionvector v as a target function in v. This estimator falls in the class of semi-parametric methods and I will denote it as Conditional Variance estimators. With simulation studies I show that the performance of the estimator is compareable to standard methods.

Guido Gazzani (WU Vienna)
"Asymptotic equivalence in the Le Cam sense"
We present in a simplified framework the contribute to statistical experiments comparison due to Prof. Dr. Lucien Le Cam. In particular we introduce the concept of Le Cam "distance" between experiments and the related tools to compute it. Such a measure of discrepancy leads us to be able to quantify, for the first time after the definition of Blackwell (1951), the loss of information when switching from a first model to another one. We show some applications both in the parametric and nonparametric regime, with particular emphasis on the latter one, leaving the discussion to a possible asymptotic equivalence between a very general jump diffusion process and its diffusion counterpart.

Jakob M. Heiss (ETH Zurich)
"How implicit regularization of neural networks affects the learned function"
Today, various forms of neural networks are trained to perform approximation tasks in many fields. However, the solutions obtained are not wholly understood. Empirical results suggest that the training favors regularized solutions. These observations motivate us to analyze properties of the solutions found by the gradient descent algorithm frequently employed to perform the training task. As a starting point, we consider one dimensional (shallow) neural networks in which weights are chosen randomly and only the terminal layer is trained. We show, that the resulting solution converges to the smooth spline interpolation of the training data as the number of hidden nodes tends to infinity. This might give valuable insight on the properties of the solutions obtained using gradient descent methods in general settings.

Jana Hlavinova (WU Vienna)
"Systemic intrinsic risk measures"
After several major collapses of financial systems, it became clear that whenmeasuring risk, one has to work with the system as a whole rather than to focuson each institution individually. In this spirit, several measures of systemicrisk were developed. We adopt a general approach of multivariate, set-valuedrisk measures of Feinstein, Rudloff and Weber (2017) and combine it with therecently proposed notion of intrinsic risk measures. In the latter, instead ofusing external capital to define the risk of a financial position, we use internalcapital, which is received when part of the currently held position is sold. Wetranslate this into a systemic framework and show that the systemic intrinsic riskmeasures have desirable properties such as monotonicity and quasi-convexity.Furthermore, for convex acceptance sets we derive dual representations of thesystemic intrinsic risk measures.

Maike Klein (FAM @ TU Wien)
"On the gain of collaboration"
We consider two companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We derive the optimal strategy for the collaboration and the minimal ruin probability if the transfer rate can exceed the drift rates in the case of independent as well as perfectly positively correlated Brownian motions. This talk is based on a joint work with Peter Grandits (TU Wien).

Verena Köck (WU Vienna)
"Solving high-dimensional parabolic partial differential equations with deep learning"
High-dimensional PDEs appear in many fields, such as physics, engineering and finance. Even though they are indispensable in many applications, their numerical solution has been a longlasting computational challenge. The feasibility of widely used finite difference methods is limited due to the "curse of dimensionality", i.e. discretizing the space-time dimension leads to an explosion of grid-points. In the last few years new techniques based on deep neural networks have gained popularity and were successfully used in many areas. Recently, the power of deep neural networks could also be extended to solve large classes of high-dimensional semilinear or nonlinear PDEs. One method makes use of the probabilistic representation of the corresponding PDE solution based on backward stochastic differential equations. In particular the gradient and the Hessian terms showing up in the BSDE are approximated with neural networks. Other methods for so-called "Kolmogorov equations" rely on the representation of PDEs as infinite dimensional stochastic optimization problems, that are spatially discretized by means of fully connected deep neural networks. In this talk, I will give an introduction to deep neural networks and discuss both methods. I will then show how they can be applied to PDEs resulting from stochastic control problems.

Gabriela Kovacova (WU Vienna)
"Acceptability Maximization"
Financial literature uses a wide variety of measures to quantify the performance of an index or a portfolio. Cherny and Madan (2009) introduced a concept of the acceptability index as a way to axiomatically define a minimal set of properties of a performance measure. Bielecki, Cialenco and Zhang (2011) extended this to the dynamic setting. In both cases acceptability indices are closely related to families of coherent risk measures. In this work we consider the problem of maximizing acceptability (or performance) over a set of available portfolios. We formulate an algorithm, applicable both in the static and the dynamic setting, which approximates the maximal acceptability via a sequence of risk minimization problems. In the dynamic setting we consider the special cases Gain loss ratio and Risk-adjusted return on capital for which we solve the acceptability maximization problem via dynamic bi-objective optimization problem.

Gudmund Pammer (University of Vienna)
"Applications of weak optimal transport and the adapted weak topology"
Optimal transport (OT) has found its way into many areas, like data science, econometrics, and mathematical finance, to name but a few. In 2018, Gozlan et. al. introduced a generalization of OT running under the name 'weak optimal transport', to be applied in the theory of geometric inequalities. Recent works show the significance and advantages of using the so-called adapted weak topology instead of the standard weak topology on the set of couplings. This presentation will familiarize you with the notion of weak OT and especially the adapted weak topology. The most important concepts and some of their applications are discussed to provide a better insight.

Mathias Pohl (University of Vienna)
"Robust risk aggregation with neural networks"
We consider settings in which the distribution of a multivariate random variable is partly ambiguous: The ambiguity lies on the level of dependence structure, and that the marginal distributions are known. We work with the set of distributions that are both close to a given reference measure in a transportation distance and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. (Joint work with Michael Kupper and Stephan Eckstein)

Dragana Radojicic (FAM @ TU Wien)
"On a binomial Limit Order Book model"
Weintroduce a Limit Order Book (LOB) model in discrete time and space, driven by a simple symmetric random walk. We study a basic but non-trivial model of the limit order book where orders get placed with a fixed displacement from the mid price and get executed whenever the mid price reaches their level. This is the joint work with Professor Friedrich Hubalek and Professor Thorsten Rheinländer. We define the key quantity, avalanche length, as an avalanche period of trade executions, but alllow a small window of size at most epsilon > 0 without any execution event. Moreover, we are interested in modeling other interesting quantities, e.g. Order Cancellations.

Katharina Riederer (FAM @ TU Wien)
"Refined Doob inequalities for σ-integrable submartingales and intertemporal risk constraints"
The main goal of this thesis is to expand the theory of martingales to σ-finite measure spaces and σ-integrable functions. First, we introduce a weakened form of integrability, the σ-integrability necessary to show the existence of conditional expectations of functions w.r.t. σ-finite measures and properties thereof. Furthermore, we introduce the eponymous term of this thesis, σ-integrable (sub-/super-)martingales. The core of the thesis consists of various generalisations and improvements of Doob’s maximum and L^p-inequalities for σ-integrable submartingales on σ-finite measure spaces. For the proofs we rely on purely deterministic inequalities. Last but not least, we discuss under what circumstances our improved inequalities hold with equality. The final chapter gives an outlook on how our improved versions of Doob’s L^p -inequalities can help practitioners in the fields of financial and actuarial mathematics.

Stefan Rigger (University of Vienna)
"Existence and (non)uniqueness of a McKean-Vlasov equation arising from contagious interactions"
We discuss existence and uniqueness of a McKean-Vlasov equation that appears as the limit of a particle system with singular, contagious interactions. Financially, the particle system in question serves as a model of default cascades in a perfectly homogeneous lending network driven by independent Brownian motions. We present an economic interpretation of the limiting equation and exhibit some open problems.
Joint work with Christa Cuchiero and Sara Svaluto-Ferro.

Philipp Schmocker (University of St. Gallen)
"Deep Stochastic Portfolio Theory"
We propose a novel machine learning application within stochastic portfolio theory (SPT), a descriptive framework for analyzing stock market structure and portfolio behaviour. By using neural networks as portfolio generating functions, we try to solve the inverse problem of SPT: Given an investment objective, is it possible to learn a generating function, which generates the optimal portfolio with the desired investment characteristics? In numerical examples, we show that our machine learning approach can recover the most well-known generating functions of SPT, and apply our method to other examples to regain the desired portfolio.
Joint work with Christa Cuchiero and Josef Teichmann.

Bertram Tschiderer (University of Vienna)
"Trajectorial Otto calculus"
We revisit the variational characterization of diffusion as entropic gradient flux, established by Jordan, Kinderlehrer, and Otto, and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of Langevin-Smoluchowski type, the Fokker-Planck probability density flow minimizes the rate of relative entropy dissipation, as measured by the distance traveled in the ambient space of probability measures with finite second moments, in terms of the quadratic Wasserstein metric. We obtain novel, stochastic-process versions of these features, valid along almost every trajectory of the diffusive motion in both the forward and, most transparently, the backward, directions of time, using a very direct perturbation analysis. By averaging our trajectorial results with respect to the underlying measure on path space, we establish the minimum rate of entropy dissipation along the Fokker-Planck flow and measure exactly the deviation from this minimum that corresponds to any given perturbation. (Joint work with Ioannis Karatzas and Walter Schachermayer)

Hanna Wutte (ETH Zurich)
"Learning from random strategies in stochastic optimal control - An approach to price the multidimensional Passport Option"
Introduced in the late 90s, the Passport Option gives its holder the right to trade in a market and receive any positive gain in the resulting traded account at maturity. Pricing the option amounts to solving a stochastic control problem, whose solution for d>=2 risky assets in the market is unknown. We address the problem by approximating the optimal multivariate strategy by universal function families. Inspired by the success of Google's AlphaGo, we propose to pre-train the network on "random expert strategies", that are realizations of random strategies whose corresponding reward exceeds a certain threshold, before improving the network via policy gradient learning. This approach, that proves to be successful in the one-dimensional case, might give valuable insights on the multivariate analytic solution.

Junjian Yang (FAM @ TU Wien)
"Random Horizon Principal-Agent Problem"
We consider a general formulation of the principal-agent problem with a continuous payment and a lump-sum payment on a random horizon. We first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation, in which case the agent’s optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. Using this approach, we reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be solved by standard methods of stochastic control theory.


 

 


Schedule

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Wednesday, November 27, 2019
seminar room DA 02B (2nd floor, yellow area)
15:00–15:15 Welcome Address
15:15–16:00 Andrew Allan (ETH Zurich)
16:00–16:30 Jana Hlavinova (WU Vienna)
16:30–17:00 Coffee Break (FAM-library, 7th floor, green area)
17:00–17:35 Guido Gazzani (WU Vienna)
17:35–18:05 Dragana Radojicic (FAM @ TU Wien)
18:05–18:35 Gabriela Kovacova (WU Vienna)
18:35–19:05 Aleksandar Arandjelovic (FAM @ TU Wien)
Thursday, November 28, 2019
FAM-library and room "Zeichensaal 3" (7th floor, green area)
10:00–12:00 Discussions & study groups
lecture hall: FH Hörsaal 2 (2nd floor, yellow area)
14:00–14:30 Hanna Wutte (ETH Zurich)
14:30–15:00 Gudmund Pammer (University of Vienna)
15:00–15:30 Stefan Rigger (University of Vienna)
15:30-16:00 Coffee break (FAM-library)
room "Zeichensaal 3" (7th floor, green area)
16:00–17:00 Walter Schachermayer (University of Vienna)
17:00–17:30 Coffee Break (FAM-library)
17:30–18:15 Junjian Yang (FAM @ TU Wien)
18:15–19:00 Maike Klein (FAM @ TU Wien)
Friday, November 29, 2019
seminar room DA 05 (5th floor, green area)
12:45–13:15 Katharina Riederer (FAM @ TU Wien)
13:15–13:45 Verena Köck (WU Vienna)
13:45–14:15 Lukas Fertl (TU Wien)
14:15–14:45 Coffee break (FAM-library)
room "Zeichensaal 3" (7th floor, green area)
14:45–15:30 Jakob M. Heiss (ETH Zurich)
15:30–16:15 Philipp Schmocker (University of St. Gallen)
16:15–16:45 Coffee break (FAM-library)
16:45–17:15 Mathias Pohl (University of Vienna)
17:15–18:00 Bertram Tschiderer (University of Vienna)
18:00–18:10 Closing Remarks
18:30–open end Joint Dinner

 

 


Social event

UNIQA Insurance Group - sponsor of the ViZuS 2019 DinnerIn or der to have time to talk to each other there will be a joint dinner in the evening of Friday, November 29, near TU Wien(18:45: Restaurant Pizzeria Riva Favorita, Favoritenstraße 4-6, 1040 Wien).

We are happy to tell you that the UNIQA Insurance Group invites all participants to the Dinner - so no costs are incurred for the participants of the Dinner!

In case you want to join the dinner please mention this during registration or write an email to the organisers.

During the dinner joint sight seeing activities on Saturday and/or Sunday can be discussed.

After the dinner everybody is invited to join the students party "Mathe-Fest" organised by the students council for mathematics "Fachschaft Mathematik" at TU Wien (no registration necessary).


 

 


Submission & Registration

Please send your application with

as soon as possible per email to the organisers.

The number of participants is limited to 30 people - registration will be closed as soon as all places are filled.
There will be no registration fee.
We regret we cannot provide meals or funding for travel or accommodation.


 

 


Freihaus building with the sculpture of Roland Goeschl

 
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