[FAM-news] reminder, this week's seminars

Sandra Trenovatz sandra at fam.tuwien.ac.at
Fri Oct 16 15:08:33 CEST 2009


Timetable

Tu, 20.10.2009, 16:30, Freihaus Hörsaal 3
(1040 Wien, Wiedner Hauptstr. 8, Freihaus, 2nd floor, yellow section)

   Giovanni Cesari (UBS Investmentbank London)
   "Modelling, Pricing, and Hedging Counterparty Credit Exposure
   (Vortragsreihe aus Finanz- und Versicherungsmathematik)
   http://www.fam.tuwien.ac.at/events/vr/20091020.php


Furthermore this time we also announce two interesting talks at 
University of Vienna:


Th, 22.10.2009, 11:15-12:15, Seminarraum S1
(1090 Wien, Althanstrasse 12)

   Patrick Cheridito (Princeton University)
   "Processes of class Sigma, last passage times and drawdowns"
   (Abstract below)


Th, 22.10.2009, 13:15, Seminarraum C 209
(1090 Wien, Nordbergstr. 15, UZA 4)

   Nicolas Vogelpoth (Vienna Institute of Finance)
   "L^0-convex Analysis and Conditional Risk Measures"
http://plone.mat.univie.ac.at/events/2009/defensio-nicolas-vogelpoth.pdf


---

Abstract of P. Cheridito's talk:
"Processes of class Sigma, last passage times and drawdowns"
(joint work with Ashkan Nikeghbali and Eckhard Platen)


We propose a general framework to study last passage times, suprema and 
drawdowns of a large class of stochastic processes. A central role in 
our approach is played by processes of class Sigma. After investigating 
convergence properties and a family of transformations that leave 
processes of class Sigma invariant, we provide three general 
representation results. The first one allows one to recover a process of 
class Sigma from its final value and the last time it visited the 
origin. In many situations this gives access to the distribution of the 
last time a stochastic process hit a certain level or was equal to its 
running maximum. It also leads to a formula recently discovered by 
Madan, Roynette and Yor expressing put option prices in terms of last 
passage times. Our second representation result is a stochastic integral 
representation of certain functionals of processes of class Sigma, and 
the third one gives a formula for their conditional expectations. From 
the latter one can deduce the laws of a variety of interesting random 
variables such as running maxima, drawdowns and maximum drawdowns of 
suitably stopped processes. As an application we discuss the pricing and 
hedging of options that depend on the running maximum of an underlying 
price process and are triggered when the underlying drops to a given 
level or alternatively, when the drawdown or relative drawdown of the 
underlying attains a given height.



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