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arXiv · 0707.3734

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

Jean-François Renaud·Bruno Rémillard
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Abstract

In this paper, we construct a Malliavin derivative for functionals of square-integrable Lévy 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 Lévy process.

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Jean-François Renaud, Bruno Rémillard. 2007-07-25. Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable Lévy process. https://arxiv.org/abs/0707.3734

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