## WK Differential Equations - Student Member:

Barbara Forster

**Address:**

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

**Email:** bforster@fam.tuwien.ac.at

**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 Lévy processes to describe the dynamics of financial data.
In the presence of Lévy 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