A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
Pham, Huyên; Langrené, Nicolas; Kharroubi, Idris (2014), A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization, Monte Carlo Methods and Applications, 20, 2, p. 145–165. http://dx.doi.org/10.1515/mcma-2013-0024
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Article accepté pour publication ou publiéLien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00905899Date
2014Nom de la revue
Monte Carlo Methods and ApplicationsVolume
20Numéro
2Éditeur
De Gruyter
Pages
145–165
Identifiant publication
Métadonnées
Afficher la notice complèteRésumé (EN)
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility, possibly degenerate. Our backward scheme, based on least-squares regressions, takes advantage of high-dimensional properties of Monte-Carlo methods, and also provides a parametric estimate in feedback form for the optimal control. A partial analysis of the error of the scheme is provided, as well as numerical tests on the problem of superreplication of option with uncertain volatilities and/or correlations, including a detailed comparison with the numerical results from the alternative scheme proposed in [7].Mots-clés
Monte-Carlo; empirical regressions; uncertain volatility; HJB equation; control randomization; Backward stochastic differential equationsPublications associées
Affichage des éléments liés par titre et auteur.
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Kharroubi, Idris; Langrené, Nicolas; Pham, Huyên (2015) Article accepté pour publication ou publié
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Aïd, René; Campi, Luciano; Langrené, Nicolas; Pham, Huyên (2014) Article accepté pour publication ou publié
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Jiao, Ying; Kharroubi, Idris; Pham, Huyen (2013) Article accepté pour publication ou publié
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Kharroubi, Idris; Pham, Huyen (2015) Article accepté pour publication ou publié
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Pham, Huyen; Kharroubi, Idris; Gassiat, Paul (2012) Article accepté pour publication ou publié