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Integration by parts formula for locally smooth laws and applications to sensitivity computations. (English) Zbl 1139.60025

The authors develop a Malliavin type calculus for functionals of the form \(F=f(V_1,\dots,V_n)\), where \(f\) is a smooth function and the \(V_i\)’s are random variables with absolutely continuous law \(p_i(y)dy\) which is assumed to be piecewise differentiable. An integration by parts formula is derived, which the authors then apply for numerical computations of sensitivities in a financial market model which is driven by a Lévy process.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60J75 Jump processes (MSC2010)
65C05 Monte Carlo methods
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