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Article: Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

TitleMaximum Principle for General Controlled Systems Driven by Fractional Brownian Motions
Authors
KeywordsBackward Differential Equations
Controlled Stochastic Differential Systems Driven By Fractional Brownian Motions
Fractional Brownian Motions
Malliavin Calculus
Maximum Principle
Partial Information Stochastic Control
Stochastic Optimal Control
Issue Date2013
PublisherSpringer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/
Citation
Applied Mathematics And Optimization, 2013, v. 67 n. 2, p. 279-322 How to Cite?
AbstractWe obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way. © 2012 Springer Science+Business Media New York.
Persistent Identifierhttp://hdl.handle.net/10722/180475
ISSN
2015 Impact Factor: 1.366
2015 SCImago Journal Rankings: 0.955
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHan, Yen_US
dc.contributor.authorHu, Yen_US
dc.contributor.authorSong, Jen_US
dc.date.accessioned2013-01-28T01:38:31Z-
dc.date.available2013-01-28T01:38:31Z-
dc.date.issued2013en_US
dc.identifier.citationApplied Mathematics And Optimization, 2013, v. 67 n. 2, p. 279-322en_US
dc.identifier.issn0095-4616en_US
dc.identifier.urihttp://hdl.handle.net/10722/180475-
dc.description.abstractWe obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way. © 2012 Springer Science+Business Media New York.en_US
dc.languageengen_US
dc.publisherSpringer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/en_US
dc.relation.ispartofApplied Mathematics and Optimizationen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBackward Differential Equationsen_US
dc.subjectControlled Stochastic Differential Systems Driven By Fractional Brownian Motionsen_US
dc.subjectFractional Brownian Motionsen_US
dc.subjectMalliavin Calculusen_US
dc.subjectMaximum Principleen_US
dc.subjectPartial Information Stochastic Controlen_US
dc.subjectStochastic Optimal Controlen_US
dc.titleMaximum Principle for General Controlled Systems Driven by Fractional Brownian Motionsen_US
dc.typeArticleen_US
dc.identifier.emailSong, J: txjsong@hku.hken_US
dc.identifier.authoritySong, J=rp01700en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1007/s00245-012-9188-7en_US
dc.identifier.scopuseid_2-s2.0-84879503444en_US
dc.identifier.hkuros220389-
dc.identifier.spage279en_US
dc.identifier.epage322en_US
dc.identifier.isiWOS:000315597300005-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridHan, Y=13605388300en_US
dc.identifier.scopusauthoridHu, Y=7407117772en_US
dc.identifier.scopusauthoridSong, J=55489918300en_US

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