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In this paper, we construct a Malliavin derivative for functionals ofsquare-integrable L\'evy processes and derive a Clark-Ocone formula. TheMalliavin derivative is defined via chaos expansions involving stochasticintegrals with respect to Brownian motion and Poisson random measure. As anillustration, we compute the explicit martingale representation for the maximumof a L\'evy process.

Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable L\'evy process