Boundary sensitivities for diffusion processes in time dependent domains

Cristina Costantini; Emmanuel Gobet; Nicole El Karoui

doi:10.1007/s00245-006-0863-4

Boundary sensitivities for diffusion processes in time dependent domains

Cristina Costantini
, Emmanuel Gobet
, Nicole El Karoui

University “G. D'Annunzio”
Ensimag, Domaine Universitaire
Ecole polytechnique

Research output: Contribution to journal › Article › peer-review

Abstract

We study the sensitivity, with respect to a time dependent domain D _s of expectations of functionals of a diffusion process stopped at the exit from D_s or normally reflected at the boundary of D _s. We establish a differentiability result and give an explicit expression for the gradient that allows the gradient to be computed by Monte Carlo methods. Applications to optimal stopping problems and pricing of American options, to singular stochastic control and others are discussed.

Original language	English
Pages (from-to)	159-187
Number of pages	29
Journal	Applied Mathematics & Optimization
Volume	54
Issue number	2
DOIs	https://doi.org/10.1007/s00245-006-0863-4
Publication status	Published - 1 Sept 2006
Externally published	Yes

Keywords

Free boundary
Monte Carlo methods
Reflected diffusion
Sensitivity analysis
Stopped diffusion
Time dependent domain

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10.1007/s00245-006-0863-4

Cite this

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AB - We study the sensitivity, with respect to a time dependent domain D s of expectations of functionals of a diffusion process stopped at the exit from Ds or normally reflected at the boundary of D s. We establish a differentiability result and give an explicit expression for the gradient that allows the gradient to be computed by Monte Carlo methods. Applications to optimal stopping problems and pricing of American options, to singular stochastic control and others are discussed.

KW - Free boundary

KW - Monte Carlo methods

KW - Reflected diffusion

KW - Sensitivity analysis

KW - Stopped diffusion

KW - Time dependent domain

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VL - 54

SP - 159

EP - 187

JO - Applied Mathematics & Optimization

JF - Applied Mathematics & Optimization

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Boundary sensitivities for diffusion processes in time dependent domains

Abstract

Keywords

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