Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable L\'evy process
Probability
2007-07-26 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0707.3734,
title = {Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable L\'evy process},
author = {Jean-François Renaud and Bruno Rémillard},
journal= {arXiv preprint arXiv:0707.3734},
year = {2007}
}
Comments
30 pages