Departement Mathematik

Talks in financial and insurance mathematics

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Herbstsemester 2009

Datum / Zeit Referent:in Titel Ort
17. September 2009
17:15-18:15
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Talks in Financial and Insurance Mathematics

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 17. September 2009, 17:15-18:15
Ort
No seminar
24. September 2009
17:15-18:15
Details

Talks in Financial and Insurance Mathematics

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 24. September 2009, 17:15-18:15
Ort
No seminar
1. Oktober 2009
17:15-18:15
Details

Talks in Financial and Insurance Mathematics

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 1. Oktober 2009, 17:15-18:15
Ort
No seminar
8. Oktober 2009
17:15-18:15 		Patrick Cheridito
Princeton University
Details

Talks in Financial and Insurance Mathematics

Titel Equilibrium pricing under translation invariant preferences
Referent:in, Affiliation Patrick Cheridito, Princeton University
Datum, Zeit 8. Oktober 2009, 17:15-18:15
Ort 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.
Equilibrium pricing under translation invariant preferencesread_more
HG G 43
15. Oktober 2009
17:15-18:15 		Toshiyuki Nakayama
Mitsubishi UFJ Securities
Details

Talks in Financial and Insurance Mathematics

Titel Support theorem for SPDE including HJM model
Referent:in, Affiliation Toshiyuki Nakayama, Mitsubishi UFJ Securities
Datum, Zeit 15. Oktober 2009, 17:15-18:15
Ort 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.
Support theorem for SPDE including HJM modelread_more
HG G 43
* 22. Oktober 2009
16:15-17:15 		Antonis Papapantoleon
TU Berlin
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Talks in Financial and Insurance Mathematics

Titel A review and some recent results in LIBOR modeling
Referent:in, Affiliation Antonis Papapantoleon, TU Berlin
Datum, Zeit 22. Oktober 2009, 16:15-17:15
Ort 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.
A review and some recent results in LIBOR modelingread_more
HG G 43
22. Oktober 2009
17:15-18:15
Details

Talks in Financial and Insurance Mathematics

Titel An Empirical Investigation of the Levy Libor Market Model
Referent:in, Affiliation
Datum, Zeit 22. Oktober 2009, 17:15-18:15
Ort 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.
An Empirical Investigation of the Levy Libor Market Modelread_more
HG G 43
29. Oktober 2009
17:15-18:15 		Nizar Touzi
Ecole Polytechnique Paris
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Talks in Financial and Insurance Mathematics

Titel Stochastic representation of $G-$martingales
Referent:in, Affiliation Nizar Touzi, Ecole Polytechnique Paris
Datum, Zeit 29. Oktober 2009, 17:15-18:15
Ort 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.
Stochastic representation of $G-$martingalesread_more
HG G 43
5. November 2009
17:15-18:15 		Martin Forde
Dublin City University
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Talks in Financial and Insurance Mathematics

Titel Small-time asymptotics for stochastic volatility models
Referent:in, Affiliation Martin Forde, Dublin City University
Datum, Zeit 5. November 2009, 17:15-18:15
Ort 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.
Small-time asymptotics for stochastic volatility modelsread_more
HG G 43
12. November 2009
17:15-18:15 		Johannes Muhle-Karbe
Universität Wien
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Talks in Financial and Insurance Mathematics

Titel A Characterization of the Martingale Property of Exponentially Affine Processes
Referent:in, Affiliation Johannes Muhle-Karbe, Universität Wien
Datum, Zeit 12. November 2009, 17:15-18:15
Ort 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.
A Characterization of the Martingale Property of Exponentially Affine Processesread_more
HG G 43
19. November 2009
17:15-18:15 		Robert Stelzer
TU München
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Talks in Financial and Insurance Mathematics

Titel Derivative Pricing and Long Memory in the Multivariate Ornstein-Uhlenbeck type Stochastic Volatility Model
Referent:in, Affiliation Robert Stelzer, TU München
Datum, Zeit 19. November 2009, 17:15-18:15
Ort 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.
Derivative Pricing and Long Memory in the Multivariate Ornstein-Uhlenbeck type Stochastic Volatility Modelread_more
HG G 43
26. November 2009
17:15-18:15 		Eberhard Mayerhofer
Vienna Institute of Finance
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Talks in Financial and Insurance Mathematics

Titel On strong solutions of positive definite jump-diffusions
Referent:in, Affiliation Eberhard Mayerhofer, Vienna Institute of Finance
Datum, Zeit 26. November 2009, 17:15-18:15
Ort 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.
On strong solutions of positive definite jump-diffusionsread_more
HG G 43
3. Dezember 2009
17:15-18:15 		Ying Hu
Université de Rennes 1
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Talks in Financial and Insurance Mathematics

Titel Ergodic BSDEs under weak dissipative assumptions and application to ergodic control
Referent:in, Affiliation Ying Hu, Université de Rennes 1
Datum, Zeit 3. Dezember 2009, 17:15-18:15
Ort 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.
Ergodic BSDEs under weak dissipative assumptions and application to ergodic controlread_more
HG G 43
10. Dezember 2009
17:15-18:15 		Walter Schachermayer
Universität Wien
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Talks in Financial and Insurance Mathematics

Titel The fundamental theorem of asset pricing for continuous processes under small transaction costs
Referent:in, Affiliation Walter Schachermayer, Universität Wien
Datum, Zeit 10. Dezember 2009, 17:15-18:15
Ort 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.
The fundamental theorem of asset pricing for continuous processes under small transaction costsread_more
HG G 43
17. Dezember 2009
17:15-18:15
Details

Talks in Financial and Insurance Mathematics

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 17. Dezember 2009, 17:15-18:15
Ort
No seminar

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Organisatoren:innen: Catherine Donnelly

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