caa a22 4500 378876511 CHVBK 20180305123421.0 cr unu---uuuuu 161128e20030401xx s 000 0 eng 10.1515/156939603322663321 doi (NATIONALLICENCE)gruyter-10.1515/156939603322663321 Optimal quadratic quantization for numerics: the Gaussian case [Elektronische Daten] [Gilles Pagès, Jacques Printems] 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. Copyright 2003, Walter de Gruyter Optimal quantization nationallicence stochastic gradient methods nationallicence numerical integration nationallicence Pagès Gilles Laboratoire de Probabilités et Modèles Aléatoires, CNRS UMR 7599, Université Paris 6, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5. E-mail: gpa@ccr.jussieu.fr aut Printems Jacques INRIA, MathFi project and Centre de Mathématiques, CNRS UMR 8050, Université Paris 12, 61, av. du Général de Gaulle, F-94010 Créteil. E-mail: printems@univ-paris12.fr aut Monte Carlo Methods and Applications Walter de Gruyter 9/2(2003-04-01), 135-165 0929-9629 9:2<135 2003 9 mcma https://doi.org/10.1515/156939603322663321 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939603322663321 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pagès Gilles Laboratoire de Probabilités et Modèles Aléatoires, CNRS UMR 7599, Université Paris 6, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5. E-mail: gpa@ccr.jussieu.fr aut NATIONALLICENCE 700 1- Printems Jacques INRIA, MathFi project and Centre de Mathématiques, CNRS UMR 8050, Université Paris 12, 61, av. du Général de Gaulle, F-94010 Créteil. E-mail: printems@univ-paris12.fr aut NATIONALLICENCE 773 0- Monte Carlo Methods and Applications Walter de Gruyter 9/2(2003-04-01), 135-165 0929-9629 9:2<135 2003 9 mcma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter