WK Differential Equations - Student Member:
Department of Financial and Actuarial Mathematics
Vienna University of Technology
Wiedner Hauptstrasse 8-10 / 105-1
A-1040 Wien, Austria
Telephone: (+43 1) 58801 10531
Fax: (+43 1) 58801 10599
Advisor: Walter Schachermayer
Co-advisor: Josef Teichmann
Research: My area of research is Stochastic Analysis, particularly the interplay with Mathematical Finance.
We are mainly interested in the approximation
of expected values on Wiener space: for a given parabolic PDE, there is a mathematical equivalence between
solving this differential equation and "the integration" of certain functionals on Wiener space. In finite
dimension, cubature can be a very efficient approach to integration. I study the appropriate extension of this
method to Wiener space. Polynomials are therefore replaced by iterated Stratonovich integrals.
The algorithmic determination of the weights and paths with finite total variation, which define a cubature
formula on Wiener space, is one of the topics of my PhD thesis. For instance, one can use a non-commutative invariance principle in order to approximate the solutions of stochastic differential equations.
Furthermore, I deal with Interest Rate Models employing LÚvy processes to describe the dynamics of financial data.
In the presence of LÚvy jumps, a unique risk neutral measure is difficult to derive and the market is therefore
generally incomplete. I currently study situations in which one can determine a unique martingale measure that is
consistent with the no arbitrage conditions.
Diploma Thesis: Cubature Formulas on Wiener Space. Advisor: Josef Teichmann