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

1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : 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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https://hal.inria.fr/inria-00070439
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:29:21 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:07 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:13:34 PM

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• HAL Id : inria-00070439, version 1

### Citation

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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