On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Handle URI:
http://hdl.handle.net/10754/336769
Title:
On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks
Authors:
Annunziato, Mario; Borzì, Alfio; Nobile, Fabio; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks 2014, 05 (16):2476 Applied Mathematics
Publisher:
Scientific Research Publishing, Inc,
Journal:
Applied Mathematics
Issue Date:
1-Sep-2014
DOI:
10.4236/am.2014.516239
Type:
Article
ISSN:
2152-7385; 2152-7393
Sponsors:
Supported in part by the European Union under Grant Agreement “Multi-ITN STRIKE-Novel Methods in Computational Finance”. Fund Project No. 304617 Marie Curie Research Training Network.
Additional Links:
http://www.scirp.org/journal/PaperDownload.aspx?DOI=10.4236/am.2014.516239
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAnnunziato, Marioen
dc.contributor.authorBorzì, Alfioen
dc.contributor.authorNobile, Fabioen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2014-12-07T12:07:12Z-
dc.date.available2014-12-07T12:07:12Z-
dc.date.issued2014-09-01en
dc.identifier.citationOn the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks 2014, 05 (16):2476 Applied Mathematicsen
dc.identifier.issn2152-7385en
dc.identifier.issn2152-7393en
dc.identifier.doi10.4236/am.2014.516239en
dc.identifier.urihttp://hdl.handle.net/10754/336769en
dc.description.abstractIn the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.en
dc.description.sponsorshipSupported in part by the European Union under Grant Agreement “Multi-ITN STRIKE-Novel Methods in Computational Finance”. Fund Project No. 304617 Marie Curie Research Training Network.en
dc.language.isoenen
dc.publisherScientific Research Publishing, Inc,en
dc.relation.urlhttp://www.scirp.org/journal/PaperDownload.aspx?DOI=10.4236/am.2014.516239en
dc.rightsThis work is licensed under the Creative Commons Attribution International License (CC BY).en
dc.subjectHamilton-Jacobi-Bellman Equationen
dc.subjectFokker-Planck Equationen
dc.subjectOptimal Control Theoryen
dc.subjectStochastic Differential Equationsen
dc.subjectHybrid Systemsen
dc.titleOn the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworksen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalApplied Mathematicsen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDipartimento di Matematica, Università degli Studi di Salerno, Fisciano, Italyen
dc.contributor.institutionInstitut für Mathematik, Universität Würzburg, Würzburg, Germanyen
dc.contributor.institutionÉcole Polytechnique Fédérale de Lausanne, Lausanne, Switzerlanden
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorTempone, Raulen
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