• G. PAGÈS
• J. PRINTEMS

Code(s) de Classification MSC:

• 94A29 Source coding [See also 68P30]
• 62L20 Stochastic approximation
• 65D30 Numerical integration
• 65D32 Quadrature and cubature formulas
• 90C59 Approximation methods and heuristics
• 90C52 Methods of reduced gradient type
• 91B28 Finance, portfolios, investment

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