The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 17, Number 1 (2007), 33-66.
Integration by parts formula for locally smooth laws and applications to sensitivity computations
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.
Ann. Appl. Probab., Volume 17, Number 1 (2007), 33-66.
First available in Project Euclid: 13 February 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60J75: Jump processes
Secondary: 65C05: Monte Carlo methods
Bally, Vlad; Bavouzet, Marie-Pierre; Messaoud, Marouen. Integration by parts formula for locally smooth laws and applications to sensitivity computations. Ann. Appl. Probab. 17 (2007), no. 1, 33--66. doi:10.1214/105051606000000592. https://projecteuclid.org/euclid.aoap/1171377176