A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
dc.contributor.author | Pham, Huyên | |
dc.contributor.author | Langrené, Nicolas
HAL ID: 171091 ORCID: 0000-0001-7601-4618 | |
dc.contributor.author | Kharroubi, Idris | |
dc.date.accessioned | 2013-11-27T15:39:20Z | |
dc.date.available | 2013-11-27T15:39:20Z | |
dc.date.issued | 2014 | |
dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/12195 | |
dc.language.iso | en | en |
dc.subject | Monte-Carlo | en |
dc.subject | empirical regressions | en |
dc.subject | uncertain volatility | en |
dc.subject | HJB equation | en |
dc.subject | control randomization | en |
dc.subject | Backward stochastic differential equations | en |
dc.subject.ddc | 332 | en |
dc.subject.classificationjel | C61 | en |
dc.subject.classificationjel | C63 | en |
dc.title | A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization | en |
dc.type | Article accepté pour publication ou publié | |
dc.contributor.editoruniversityother | Laboratoire 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.editoruniversityother | Centre 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.abstracten | 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]. | en |
dc.relation.isversionofjnlname | Monte Carlo Methods and Applications | |
dc.relation.isversionofjnlvol | 20 | |
dc.relation.isversionofjnlissue | 2 | |
dc.relation.isversionofjnldate | 2014 | |
dc.relation.isversionofjnlpages | 145–165 | |
dc.relation.isversionofdoi | http://dx.doi.org/10.1515/mcma-2013-0024 | |
dc.identifier.urlsite | http://hal.archives-ouvertes.fr/hal-00905899 | en |
dc.relation.isversionofjnlpublisher | De Gruyter | |
dc.subject.ddclabel | Economie financière | en |
dc.description.submitted | non | en |
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