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Article: Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions
Title | Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions |
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Authors | |
Keywords | Backward 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 Date | 2013 |
Publisher | Springer 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? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/180475 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 0.916 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Han, Y | en_US |
dc.contributor.author | Hu, Y | en_US |
dc.contributor.author | Song, J | en_US |
dc.date.accessioned | 2013-01-28T01:38:31Z | - |
dc.date.available | 2013-01-28T01:38:31Z | - |
dc.date.issued | 2013 | en_US |
dc.identifier.citation | Applied Mathematics And Optimization, 2013, v. 67 n. 2, p. 279-322 | en_US |
dc.identifier.issn | 0095-4616 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/180475 | - |
dc.description.abstract | We 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.language | eng | en_US |
dc.publisher | Springer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/ | en_US |
dc.relation.ispartof | Applied Mathematics and Optimization | en_US |
dc.subject | Backward Differential Equations | en_US |
dc.subject | Controlled Stochastic Differential Systems Driven By Fractional Brownian Motions | en_US |
dc.subject | Fractional Brownian Motions | en_US |
dc.subject | Malliavin Calculus | en_US |
dc.subject | Maximum Principle | en_US |
dc.subject | Partial Information Stochastic Control | en_US |
dc.subject | Stochastic Optimal Control | en_US |
dc.title | Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions | en_US |
dc.type | Article | en_US |
dc.identifier.email | Song, J: txjsong@hku.hk | en_US |
dc.identifier.authority | Song, J=rp01700 | en_US |
dc.description.nature | postprint | en_US |
dc.identifier.doi | 10.1007/s00245-012-9188-7 | en_US |
dc.identifier.scopus | eid_2-s2.0-84879503444 | en_US |
dc.identifier.hkuros | 220389 | - |
dc.identifier.spage | 279 | en_US |
dc.identifier.epage | 322 | en_US |
dc.identifier.isi | WOS:000315597300005 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Han, Y=13605388300 | en_US |
dc.identifier.scopusauthorid | Hu, Y=7407117772 | en_US |
dc.identifier.scopusauthorid | Song, J=55489918300 | en_US |
dc.identifier.issnl | 0095-4616 | - |