Minimum variance importance sampling via Population Monte Carlo
CMAP, École Polytechnique, Palaiseau, France; firstname.lastname@example.org
2 École Centrale Marseille and LATP, France; email@example.com
3 Projet , INRIA Futurs, Université Paris-Sud, France; firstname.lastname@example.org
4 CEREMADE, Université Paris Dauphine and CREST, INSEE, Paris, France; email@example.com
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.
Mathematics Subject Classification: 60F05 / 62L12 / 65-04 / 65C05 / 65C40 / 65C60
Key words: Adaptivity / Cox-Ingersoll-Ross model / Euler scheme / importance sampling / mathematical finance / mixtures / moderate deviations / population Monte Carlo / variance reduction.
© EDP Sciences, SMAI, 2007