Optimal quadratic quantization for numerics: the Gaussian case
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| 024 | 7 | 0 | |a 10.1515/156939603322663321 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/156939603322663321 | ||
| 245 | 0 | 0 | |a Optimal quadratic quantization for numerics: the Gaussian case |h [Elektronische Daten] |c [Gilles Pagès, Jacques Printems] |
| 520 | 3 | |a 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. | |
| 540 | |a Copyright 2003, Walter de Gruyter | ||
| 690 | 7 | |a Optimal quantization |2 nationallicence | |
| 690 | 7 | |a stochastic gradient methods |2 nationallicence | |
| 690 | 7 | |a numerical integration |2 nationallicence | |
| 700 | 1 | |a Pagès |D Gilles |u 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 |4 aut | |
| 700 | 1 | |a Printems |D Jacques |u 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 |4 aut | |
| 773 | 0 | |t Monte Carlo Methods and Applications |d Walter de Gruyter |g 9/2(2003-04-01), 135-165 |x 0929-9629 |q 9:2<135 |1 2003 |2 9 |o mcma | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/156939603322663321 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/156939603322663321 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Pagès |D Gilles |u 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 |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Printems |D Jacques |u 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 |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Monte Carlo Methods and Applications |d Walter de Gruyter |g 9/2(2003-04-01), 135-165 |x 0929-9629 |q 9:2<135 |1 2003 |2 9 |o mcma | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||