Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5879
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dc.contributorDepartment of Applied Mathematics-
dc.creatorBuckdahn, R-
dc.creatorHuang, J-
dc.creatorLi, J-
dc.date.accessioned2014-12-11T08:24:22Z-
dc.date.available2014-12-11T08:24:22Z-
dc.identifier.issn0363-0129-
dc.identifier.urihttp://hdl.handle.net/10397/5879-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2012 Society for Industrial and Applied Mathematicsen_US
dc.subjectBackward stochastic differential equationen_US
dc.subjectHJB equationen_US
dc.subjectLipschitz continuityen_US
dc.subjectReflected backward stochastic differential equationsen_US
dc.subjectSemiconcavityen_US
dc.subjectValue functionen_US
dc.titleRegularity properties for general HJB equations : a backward stochastic differential equation methoden_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage1466-
dc.identifier.epage1501-
dc.identifier.volume50-
dc.identifier.issue3-
dc.identifier.doi10.1137/110828629-
dcterms.abstractIn this work we investigate regularity properties of a large class of Hamilton–Jacobi–Bellman (HJB) equations with or without obstacles, which can be stochastically interpreted in the form of a stochastic control system in which nonlinear cost functional is defined with the help of a backward stochastic differential equation (BSDE) or a reflected BSDE. More precisely, we prove that, first, the unique viscosity solution V (t, x) of an HJB equation over the time interval [0, T], with or without an obstacle, and with terminal condition at time T, is jointly Lipschitz in (t, x) for t running any compact subinterval of [0, T). Second, for the case that V solves an HJB equation without an obstacle or with an upper obstacle it is shown under appropriate assumptions that V (t, x) is jointly semiconcave in (t, x). These results extend earlier ones by Buckdahn, Cannarsa, and Quincampoix [Nonlinear Differential Equations Appl., 17 (2010), pp. 715–728]. Our approach embeds their idea of time change into a BSDE analysis. We also provide an elementary counterexample which shows that, in general, for the case that V solves an HJB equation with a lower obstacle the semiconcavity doesn’t hold true.-
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on control and optimization, 2012, v. 50, no. 3, p. 1466–1501-
dcterms.isPartOfSIAM Journal on control and optimization-
dcterms.issued2012-
dc.identifier.isiWOS:000305961400017-
dc.identifier.scopus2-s2.0-84865522869-
dc.identifier.eissn1095-7138-
dc.identifier.rosgroupidr56440-
dc.description.ros2011-2012 > Academic research: refereed > Publication in refereed journal-
dc.description.oaVersion of Recorden_US
dc.identifier.FolderNumberOA_IR/PIRAen_US
dc.description.pubStatusPublisheden_US
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