15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 10 - Angewandte Mathematik, Industrie- und Finanzmathematik
Dienstag, 18. September 2001, 17.30, Hörsaal 42


Interest rate theory and infinite-dimensional geometry

Josef Teichmann, TU Wien (Koautor: Damir Filipovic)

The Heath-Jarrow-Morton-equation fits in the framework of Stochastic Differential Equations with values in Hilbert spaces. It is natural to ask, whether the associated Heath-Jarrow-Morton-equation admits a stochastic flow leaving finite dimensional submanifolds invariant (Finite dimensional Realizations, FDRs for short). This is due to the fact, that statistical observations shall be possible with respect to the term structure of interest rates. Viability conditions of Nagumo-type have been derived by Damir Filipovic. Tomas Björk and Lars Svensson gave sufficient and necessary conditions for the existence of FDRs within a particular Hilbert space setup. Recently modern methods of differential geometry in infinite dimensions have been applied to solve the existence problem in general, namely Frobenius theory on Fréchet spaces inspired by convenient calculus in the sense of Kriegl-Michor. The result is that FDRs have a particularly simple geometry and can be classified under weak assumptions.

E-Mail: josef.teichmann@fam.tuwien.ac.at
Homepage: www.fam.tuwien.ac.at/~jteichma

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