A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization

Idris Kharroubi (), Nicolas Langrené () and Huyên Pham ()
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Idris Kharroubi: Mathématiques de l'économie et de la finance - CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Nicolas Langrené: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, EDF R&D - EDF R&D - EDF - EDF
Huyên Pham: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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].

Keywords: Backward stochastic differential equations; control randomization; HJB equation; uncertain volatility; empirical regressions; Monte-Carlo (search for similar items in EconPapers)
Date: 2013-11-18
New Economics Papers: this item is included in nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-00905899

DOI: 10.1515/mcma-2013-0024

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