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START Project "Geometry of Stochastic Differential Equations" by Josef Teichmann

The START Prize is awarded by the Austrian Science Fund (FWF) on behalf of the Federal Ministry for Education, Science and Culture (BM:BWK).

My START-project is called "Geometry of Stochastic Differential Equations". See also the START-Portal for details on this Start-project. This project and its research group will be located at FAM at Vienna University of Technology.

As often in science, a project is best explained by giving examples of problems, which I have in mind:

term structure of interest rates

During our research we plan to investigate the following fields based upon several key publications. See my publications at the respective number.

FDR for Levy-driven Stochastic Differential Equations in infinite dimensions

[7] Damir Filipovic, Josef Teichmann: Existence of invariant Manifolds for Stochastic Equations in infinite dimension, Journal of Functional Analysis 197, 398-432, 2003.

[8] Josef Teichmann: A Frobenius Theorem on convenient manifolds, Monatshefte für Mathematik 134, 159-167, 2001.

[12] Friedrich Hubalek, Irene Klein, Josef Teichmann: A general proof of the Dybvig-Ingersoll-Ross-Theorem: Long forward rates can never fall, Mathematical Finance 12 (4), 447-451, 2002.

[13] Damir Filipovic, Josef Teichmann: Regularity of Finite-dimensional Realizations for Evolution Equations, Journal of Functional Analysis 197, 433-446, 2003.

[14] Damir Filipovic, Josef Teichmann: On the Geometry of the Term structure of Interest Rates, Proceedings of the Royal Society London A 460, 129-167, 2004.

Hypo-ellipticity in mathematical Finance

[15] Fabrice Baudoin, Josef Teichmann: Hypoellipticity in infinite dimensions and an application to interest rate theory, Annals of applied Probability 15 (3), 1765-1777, 2005.

Distributional Properties of  Iterated Stratonovich Integrals

[19] Josef Teichmann: Calculating the Greeks by Cubature formulas, Proceedings of the Royal Society London A 462, 647-670, 2006.

Hedging in Finite Factor Models

[22] Barbara Forster, Eva Lütkebohmert, Josef Teichmann: Calculation of Greeks for Jump-Diffusions, submitted, 2006.

Numerical Probability Theory (Cubature Methods, Simulation of Iterated Stratonvich Integrals)

[19] Josef Teichmann: Calculating the Greeks by Cubature formulas, Proceedings of the Royal Society London A 462, 647-670, 2006.

Optimal Transportation

[23] Walter Schachermayer, Josef Teichmann: Characterization of optimal Transport Plans for the Monge-Kantorovich-Problem, Proceedings of the AMS, to appear, 2006.