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Malliavin's Calculus and...

Malliavin's Calculus and Applications In Stochastic Control and Finance

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
33,00 zł