# Talks in Financial and Insurance Mathematics

This is the regular weekly research seminar on Insurance Mathematics and Stochastic Finance.

## Autumn Semester 2009

Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Date / Time Speaker Title Location
17 September 2009
17:15-18:15
No seminar
24 September 2009
17:15-18:15
No seminar
1 October 2009
17:15-18:15
No seminar
8 October 2009
17:15-18:15
Patrick Cheridito
Princeton University
HG G 43
Abstract: I give conditions for the existence and uniqueness of equilibria in incomplete dynamic market models when agents have translation invariant preferences. This includes mean-variance type preferences and expected exponential utility. General results are provided in discrete time. Then a special case is discussed where equilibrium prices can be represented as solutions to a system of backward stochastic difference equations. In the continuous-time limit, a system of coupled backward stochastic differential equations with quadratic drivers appears.
15 October 2009
17:15-18:15
Toshiyuki Nakayama
Mitsubishi UFJ Securities
HG G 43
Abstract: A support theorem will be shown for the mild solution of the SDE in a Hilbert space of the form dX(t) = A X(t) dt + b(X(t)) dt + σ(X(t)) dB(t) where B(t) is a Hilbert space-valued Wiener process and A is a infinitesimal generator for (C0)-semigroup of bounded linear operators. The extension of support theorem for infinite dimensional SDE's without A was achieved in Aida, S. But our mild solutions are not necessarily expressed as strong solutions due to the existence of unbounded operator A, so our approach must be different from Aida, S. This equation contains the SPDE within HJM model for in mathematical finance. By using support theorem we can conclude a viability theorem, which is useful for "consistency problems" in interest rate models.
* 22 October 2009
16:15-17:15
Antonis Papapantoleon
TU Berlin
HG G 43
Abstract: In this talk, we first describe some Axioms that models for LIBOR rates should satisfy, and then present some popular approaches to LIBOR modeling, namely LIBOR market models and forward price models. We briefly review the construction of these models, discuss if they satisfy the aforementioned Axioms, and describe the problems that arise. Finally, we describe some methods to overcome these problems.
22 October 2009
17:15-18:15
David Skovmand
University of Aarhus
HG G 43
Abstract: In this talk we analyze the Levy Market Model, originally proposed by Eberlein & Ozkan (05), with an emphasis on the optimal choice of the driving process. Using a large time series of data on EURIBOR caps, a variety of driving processes are subjected to a performance analysis. The processes investigated include standard jump-diffusion processes in the Merton sense, time-changed Levy processes, and selfsimilar additive processes also known as Sato processes. We find that models with a high frequency component appear to provide the best fit to the data and Sato processes in particular yield impressive results despite their parsimony.
29 October 2009
17:15-18:15
Nizar Touzi
Ecole Polytechnique Paris
HG G 43
Abstract: Using our standard stochastic analysis approach to quasi-sure analysis, we revisit the theory of $G-$expectations and $G-$martingales introduced recently by Peng. Our approach allows to extend these notions in a larger space and, more importantly, to solve the open problem of $G-$martingale representation.
5 November 2009
17:15-18:15
Martin Forde
Dublin City University
HG G 43
Abstract: We derive the correction term for call options and implied volatility under the Heston model in the small-maturity limit, using Laplace's method for contour integrals developed by Olver. We find that the Out-of-the-money and At-the-money call option expansions are qualitatively different (this is joint work with Antoine Jacquier and Roger Lee). I also discuss call option asymptotics for a general stochastic volatility model, using the Heat kernel expansion.
12 November 2009
17:15-18:15
Johannes Muhle-Karbe
Universität Wien
HG G 43
Abstract: We consider local martingales of exponential form M = exp(X) or E(X) where X denotes one component of a multivariate affine process in the sense of Duffie, Filipovic and Schachermayer (2003). By completing the characterization of conservative affine processes, we give deterministic and sufficient conditions in terms of the parameters of X for M to be a true martingale. This is joint work with Eberhard Mayerhofer and Alexander Smirnov.
19 November 2009
17:15-18:15
Robert Stelzer
TU München
HG G 43
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 Lévy 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.
26 November 2009
17:15-18:15
Eberhard Mayerhofer
Vienna Institute of Finance
HG G 43
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.
3 December 2009
17:15-18:15
Ying Hu
Université de Rennes 1
HG G 43
Abstract: In this paper we study ergodic backward stochastic differential equations (BSDEs) under weak dissipative assumptions. On the one hand, we show the existence of solution to the ergodic BSDE by use of coupling estimates for perturbed forward stochastic differential equations. On the other hand, we show the uniqueness of solution to the associated Hamilton-Jacobi-Bellman equation by use of the recurrence for perturbed forward stochastic differential equations. Applications are given to the optimal ergodic control of stochastic partial differential equations to illustrate our results. This is a joint work with Arnaud Debussche and Gianmario Tessitore.
10 December 2009
17:15-18:15
Walter Schachermayer
Universität Wien
HG G 43
Abstract: A version of the fundamental theorem of asset pricing is proved for continuous asset prices with small proportional transaction costs. Equivalence is established between: (a) the absence of arbitrage with general strategies for arbitrarily small transaction costs $\varepsilon > 0$, (b) the absence of free lunches with bounded risk for arbitrarily small transaction costs $\varepsilon > 0$, and (c) the existence of $\varepsilon$-consistent price systems -- the analogue of martingale measures under transaction costs -- for arbitrarily small $\varepsilon > 0$. The proof proceeds through an explicit construction, as opposed to the usual separation arguments. The paper concludes comparing numéraire-free and numéraire-based notions of admissibility, and the corresponding martingale and local martingale properties for consistent price systems.
17 December 2009
17:15-18:15
No seminar

Organizers: Catherine Donnelly

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Wed Jun 28 23:03:46 CEST 2017
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