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Functional quantization based stratified sampling methods

Sylvain Corlay 1, Pagès Gilles 1

(15/03/2010)

In this article, we propose several quantization based stratified sampling methods to reduce the variance of a Monte-Carlo simulation. Theoretical aspects of stratification lead to a strong link between the problem of optimal $L^2$-quantization of a random variable and the variance reduction that can be achieved. We first emphasize on the consistency of quantization for designing strata in stratified sampling methods in both finite dimensional and infinite dimensional frameworks. We show that this strata design has a uniform efficiency among the class of Lipschitz continuous functionals. Then a stratified sampling algorithm based on product functional quantization is proposed for path-dependent functionals of multi-factor diffusions. The method is also available for processes made of other Gaussian processes as the Brownian bridge or an Ornstein-Uhlenbeck process. The balance between the algorithmic complexity of the simulation and the variance reduction factor has also been studied.

1 :	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot

Domaine

:

Mathématiques/Probabilités

Mots Clés : functional quantization – vector quantization – stratification – variance reduction – Monte-Carlo simulation – Karhunen-Loève basis – Gaussian process – Brownian motion – Brownian bridge – fractional Brownian motion – principal component analysis – numerical integration – option pricing – Voronoi diagram – product quantizer

hal-00464088, version 1

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Contributeur : Sylvain Corlay <>

Soumis le : Lundi 15 Mars 2010, 20:10:47

Dernière modification le : Vendredi 19 Mars 2010, 11:15:44