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Heath Lectures In Probability and Mathematical Finance
Introduction to Malliavin Calculus and its
Applications
Josef Teichmann, Vienna University of Technology
May 11-16, 2009, 2:00-5:00 PM, Porter Hall Room 226B.
Plan of the lectures.
- Introduction of three leading examples for the course
(stochastic Taylor expansion and numerics of S(P)DEs, Hypo-ellipticity and invariance, Greeks in mathematical Finance)
- Basic definitions of Malliavin calculus (Malliavin derivative, Skorohod integral, Clark-Ocone formula, Malliavin matrix)
- S(P)DEs, first variation processes, absolute continuity, invariance of sets with respect to S(P)DEs
- Hormander-Malliavin hypo-ellipticity results and applications to mathematical finance (Greeks)
- Hypo-ellipticity and Cubature on Wiener space for S(P)DEs
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