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Article Dans Une Revue Communications in Mathematical Sciences Année : 2010

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

Résumé

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.

Dates et versions

hal-00402702 , version 1 (08-07-2009)

Identifiants

Citer

Sébastien Boyaval, Tony Lelièvre. A Variance Reduction Method for Parametrized Stochastic Differential Equations using the Reduced Basis Paradigm. Communications in Mathematical Sciences, 2010, 8 (3), pp.735-762. ⟨10.4310/CMS.2010.v8.n3.a7⟩. ⟨hal-00402702⟩
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