Parabolic Bellman Equations with Risk Control

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dc.contributor.ISNI0000000113231180 (Bensoussan, A)
dc.contributor.ORCID0000-0003-0743-498X (Bensoussan, A)
dc.contributor.authorBensoussan, Alain
dc.contributor.authorBreit, D.
dc.contributor.authorFrehse, J.
dc.contributor.utdAuthorBensoussan, Alain
dc.date.accessioned2019-06-28T19:02:45Z
dc.date.available2019-06-28T19:02:45Z
dc.date.created2018-04-17
dc.description.abstractWe consider stochastic optimal control problems with an additional term representing the variance of the control functions. The latter one may serve as a risk control. We present and treat the problem in a purely analytical way via a Vlasov-McKean functional and Bellman equations with mean field dependence. We obtain global existence and, essentially, optimal global regularity for the solutions of the Bellman equation and the minimizing control. Surprisingly, the risk term simplifies the analysis to a certain extend.
dc.identifier.bibliographicCitationBensoussan, A., D. Breit, and J. Frehse. 2018. "Parabolic bellman equations with risk control." SIAM Journal on Control and Optimization 56(2): 1535-1549.
dc.identifier.issn0363-0129
dc.identifier.issue2
dc.identifier.urihttps://hdl.handle.net/10735.1/6641
dc.identifier.volume56
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics Publications
dc.relation.urihttp://dx.doi.org/10.1137/17M1122839
dc.rights©2018 Society for Industrial and Applied Mathematics Publications
dc.source.journalSIAM Journal on Control and Optimization
dc.subjectMean field theory
dc.subjectLoss control
dc.subjectDynamic programming
dc.subjectRisk assessment
dc.subjectStochastic systems
dc.subjectDifferential equations, Parabolic
dc.subjectStochastic differential equations
dc.subjectStochastic control theory
dc.titleParabolic Bellman Equations with Risk Control
dc.type.genrearticle

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