| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 427 - 447 | |
| DOI | https://doi.org/10.1051/ps:2007028 | |
| Published online | 17 August 2007 | |
Minimum variance importance sampling via Population Monte Carlo
1
CMAP, École Polytechnique, Palaiseau, France; douc@cmapx.polytechnique.fr
2
École Centrale Marseille and LATP, France; guillin@cmi.univ-mrs.fr
3
Projet , INRIA Futurs, Université Paris-Sud, France; jean-michel.marin@inria.fr
4
CEREMADE, Université Paris Dauphine and CREST, INSEE, Paris, France; xian@ceremade.dauphine.fr
Received:
19
January
2007
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
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