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Minimum variance importance sampling via Population Monte Carlo

Published online by Cambridge University Press:  17 August 2007

R. Douc ,
A. Guillin ,
J.-M. Marin  and
C. P. Robert
R. Douc
Affiliation:
CMAP, École Polytechnique, Palaiseau, France; douc@cmapx.polytechnique.fr
A. Guillin
Affiliation:
École Centrale Marseille and LATP, France; guillin@cmi.univ-mrs.fr
J.-M. Marin
Affiliation:
Projet , INRIA Futurs, Université Paris-Sud, France; jean-michel.marin@inria.fr
C. P. Robert
Affiliation:
CEREMADE, Université Paris Dauphine and CREST, INSEE, Paris, France; xian@ceremade.dauphine.fr
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Abstract

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 iterativelyoptimized 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 Europeanoption 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.


Keywords

AdaptivityCox-Ingersoll-Ross modelEuler schemeimportance samplingmathematical financemixturesmoderate deviationspopulation Monte Carlovariance reduction.

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