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

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dc.creatorBally, Vlad
dc.creatorBavouzet, Marie-Pierre
dc.creatorMessaoud, Marouen
dc.date2007-02-28
dc.date.accessioned2026-07-07T07:49:23Z
dc.date.available2026-07-07T07:49:23Z
dc.descriptionWe consider random variables of the form $F=f(V_1,...,V_n)$, where $f$ is a smooth function and $V_i,i\in\mathbb{N}$, are random variables with absolutely continuous law $p_i(y) dy$. We assume that $p_i$, $i=1,...,n$, are piecewise differentiable and we develop a differential calculus of Malliavin type based on $\partial\ln p_i$. This allows us to establish an integration by parts formula $E(\partial_iϕ(F)G)=E(ϕ(F)H_i(F,G))$, 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051606000000592 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0702884
dc.identifierhttp://arxiv.org/abs/math/0702884
dc.identifierAnnals of Applied Probability 2007, Vol. 17, No. 1, 33-66
dc.identifierdoi:10.1214/105051606000000592
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124830
dc.subjectProbability
dc.subject60H07, 60J75 (Primary) 65C05 (Secondary)
dc.titleIntegration by parts formula for locally smooth laws and applications to sensitivity computations
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