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Minimum variance importance sampling via Population Monte Carlo

Douc, Randal; Guillin, Arnaud; Marin, Jean-Michel; Robert, Christian P. (2007), Minimum variance importance sampling via Population Monte Carlo, ESAIM. Probability and Statistics, 11, p. 427-447. http://dx.doi.org/10.1051/ps:2007028

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Type
Article accepté pour publication ou publié
Date
2007
Journal name
ESAIM. Probability and Statistics
Volume
11
Publisher
Cambridge University Press
Pages
427-447
Publication identifier
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Author(s)
Douc, Randal
Guillin, Arnaud
Marin, Jean-Michel cc
Robert, Christian P.
Abstract (EN)
Variance reduction has always been a central issue in Monte Carlo experiments. Population Monte Carlo can be used to this effect, in that a mixture of importance functions, called a D-kernel, can be iteratively optimized to achieve the minimum asymptotic variance for a function of interest among all possible mixtures. The implementation of this iterative scheme is illustrated for the computation of the price of a European option in the Cox-Ingersoll-Ross model. A Central Limit theorem as well as moderate deviations are established for the D-kernel Population Monte Carlo methodology.

Subjects / Keywords
Adaptivity; Cox-Ingersoll-Ross model; Euler scheme; importance sampling; mathematical finance; mixtures; moderate deviations; population Monte Carlo; variance reduction