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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00402702
Contributor : Sébastien Boyaval Connect in order to contact the contributor
Submitted on : Wednesday, July 8, 2009 - 10:13:44 AM
Last modification on : Thursday, February 3, 2022 - 11:14:19 AM

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

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