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Rapport (Rapport De Recherche) Année : 2005

Integration by parts formula for locally smooth laws and applications to sensitivity computations

Vlad Bally
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Marie-Pierre Bavouzet
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Résumé

We consider random variables of the form $F=f(V_1,...,V_n)$ where $f$ is a smooth function and $V_i,i\in\mathbbN$ are random variables with absolutely continuous law $p_i(y).$ We assume that $p_i,i=1,...,n$ are piecewise differentiable and we develop a differential calculus of Malliavin type based on $\partial\lnp_i.$ This allows us to establish an integration by parts formula $E(\partial_i\phi(F)G)=E(\phi(F)H_i(F,G))$ where $H_i(F,G)$ is a random variable constructed using the differential operators acting on $F$ and $G.$ We use this formula in order to give numerical algorithms for sensitivity computations in a model driven by a Lévy process.
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Dates et versions

inria-00070439 , version 1 (19-05-2006)

Identifiants

  • HAL Id : inria-00070439 , version 1

Citer

Vlad Bally, Marie-Pierre Bavouzet, Marouen Messaoud. Integration by parts formula for locally smooth laws and applications to sensitivity computations. [Research Report] RR-5567, INRIA. 2005, pp.54. ⟨inria-00070439⟩
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