Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable Lévy process

Details Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable Lévy process Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable Lévy process

2007-07-25

arxiv.org/abs/0707.3734v1

Mathematics

Probability

30 pages

Scientific paper

In this paper, we construct a Malliavin derivative for functionals of square-integrable L\'evy processes and derive a Clark-Ocone formula. The Malliavin derivative is defined via chaos expansions involving stochastic integrals with respect to Brownian motion and Poisson random measure. As an illustration, we compute the explicit martingale representation for the maximum of a L\'evy process.

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