Integration by Parts Formula for Locally Smooth Laws and Applications to Sensitivity Computations
نویسندگان
چکیده
We consider random variables of the form F = f(V1, . . . , Vn), where f is a smooth function and Vi, i ∈N, are random variables with absolutely continuous law pi(y)dy. We assume that pi, i= 1, . . . , n, are piecewise differentiable and we develop a differential calculus of Malliavin type based on ∂ lnpi. This allows us to establish an integration by parts formula E(∂iφ(F )G) = E(φ(F )Hi(F,G)), where Hi(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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تاریخ انتشار 2007