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Communications in Mathematical Sciences 8, 3 (2010) 735-762

A Variance Reduction Method for Parametrized Stochastic Differential Equations using the Reduced Basis Paradigm

Sébastien Boyaval 1, 2, Tony Lelièvre 1, 2

INRIA project MICMAC Collaboration(s)

(2010)

In this work, we develop a reduced-basis approach for the efficient computation of parametrized expected values, for a large number of parameter values, using the control variate method to reduce the variance. Two algorithms are proposed to compute online, through a cheap reduced-basis approximation, the control variates for the computation of a large number of expectations of a functional of a parametrized Ito stochastic process (solution to a parametrized stochastic differential equation). For each algorithm, a reduced basis of control variates is pre-computed offline, following a so-called greedy procedure, which minimizes the variance among a trial sample of the output parametrized expectations. Numerical results in situations relevant to practical applications (calibration of volatility in option pricing, and parameter-driven evolution of a vector field following a Langevin equation from kinetic theory) illustrate the efficiency of the method.

1 :	MICMAC (INRIA Paris - Rocquencourt)
	Ecole des Ponts ParisTech – INRIA
2 :	Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
	INRIA – Ecole des Ponts ParisTech

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : Variance Reduction – Stochastic Differential Equations – Reduced-Basis Methods

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Contributeur : Sébastien Boyaval <>

Soumis le : Mercredi 8 Juillet 2009, 10:13:44

Dernière modification le : Mercredi 7 Septembre 2011, 14:59:54