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Gilles Pags, Jacques Printems

Optimal quadratic quantization for numerics: the Gaussian case

Keywords: Optimal quantization, stochastic gradient methods, Numerical Integration

Optimal quantization has been recently revisited in multi-dimensional numerical integration, multi-asset American option pricing, control theory and nonlinear filtering theory. In this paper, we enlighten some numerical procedures in order to get some accurate optimal quadratic quantization of the Gaussian distribution in one and higher dimensions. We study in particular Newton method in the deterministic case (dimension d = 1) and stochastic gradient in higher dimensional case (d ≥ 2). Some heuristics are provided which concern the step in the stochastic gradient method. Finally numerical examples borrowed from mathematical finance are used to test the accuracy of our Gaussian optimal quantizers.

Monte Carlo Methods and Applications, Walter de Gruyter

Print ISSN: 0929-9629
Volume: 9, 04/2003
Pages: 135 - 165

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