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

dc.contributor.authorPham, Huyên
dc.contributor.authorLangrené, Nicolas
HAL ID: 171091
ORCID: 0000-0001-7601-4618
dc.contributor.authorKharroubi, Idris
dc.date.accessioned2013-11-27T15:39:20Z
dc.date.available2013-11-27T15:39:20Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12195
dc.language.isoenen
dc.subjectMonte-Carloen
dc.subjectempirical regressionsen
dc.subjectuncertain volatilityen
dc.subjectHJB equationen
dc.subjectcontrol randomizationen
dc.subjectBackward stochastic differential equationsen
dc.subject.ddc332en
dc.subject.classificationjelC61en
dc.subject.classificationjelC63en
dc.titleA numerical algorithm for fully nonlinear HJB equations: an approach by control randomizationen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire de Probabilités et Modèles Aléatoires (LPMA) http://www.proba.jussieu.fr/ CNRS : UMR7599 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot;France
dc.contributor.editoruniversityotherCentre de Recherche en Économie et Statistique (CREST) http://www.crest.fr/ INSEE – École Nationale de la Statistique et de l'Administration Économique;France
dc.description.abstractenWe 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].en
dc.relation.isversionofjnlnameMonte Carlo Methods and Applications
dc.relation.isversionofjnlvol20
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages145–165
dc.relation.isversionofdoihttp://dx.doi.org/10.1515/mcma-2013-0024
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00905899en
dc.relation.isversionofjnlpublisherDe Gruyter
dc.subject.ddclabelEconomie financièreen
dc.description.submittednonen


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