Malliavin's calculus and applications in stochastic control and finance

Peter ImkellerIM PAN Lecture Notes, Vol. 1, Warsaw 2008, ISBN: 978-83-86806-02-7, 83 pp.

About the book: 
Malliavin's calculus alias the stochastic calculus of variations nowadays finds numerous applications in stochastic analysis and finance, ranging from enhancements of the speed of convergence of Monte-Carlo algorithms for stochastic equations to the fine structure of solutions of stochastic control problems in backward stochastic differential equations (BSDE). We develop this calculus by starting with everybody's notion of differential calculus on finite dimensional Euclidean space. We generalize it to infinite dimensional sequence space, and use a natural isomorphism between sequence and path space to carry it over to canonical Wiener space. In a generalized version of the Clark-Ocone representation formula it is seen to provide the right framework to interpret solutions of BSDE.

About the authors: 
Peter Imkeller is professor for Probability at Humboldt-Universität zu Berlin since 1996. His main areas of interest range from stochastic analysis and dynamics, with a particular focus in the statistical and probabilistic analysis of metastability in paleo-climatic time series and low-dimensional climate models, to stochastic finance, with a focus on risk assessment in insurance and environment.

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