2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124830We 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.Published 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)Probability60H07, 60J75 (Primary) 65C05 (Secondary)text