Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Optimal quadratic quantization for numerics : the Gaussian case


Code(s) de Classification MSC:

Résumé: Optimal quantization has been recently revisited in multi-dimensional numerical integration (see [18]), multi-asset American option pricing (see [1]), Control Theory (see [19]) and Nonlinear Filtering Theory (see [20]). In this paper, we enlighten some numerical procedures in order to get some accurate optimal quadratic quantization of the Gaussian distribution in higher dimension. We study in particular Newton method in the deterministic case (dimension $d=1$) and stochastic gradient in higher dimensional case ($d \geq 2$). Some heuristics are provided which concern the step in the stochastic gradient method. Finally numerical examples borrowed to mathematical finance are used to test the accuracy of our Gaussian optimal quantizers.

Mots Clés: Optimal quantization ; stochastic gradient methods ; numerical integration

Date: 2003-03-20

Prépublication numéro: PMA-809

Front pages : PMA-809.dvi

Second version : PMA-809Bis.pdf