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A SECOND-ORDER STOCHASTIC MAXIMUM PRINCIPLE FOR GENERALIZED MEAN-FIELD SINGULAR CONTROL PROBLEM
Guo, Hancheng; Xiong, Jie
2018-06
Source PublicationMATHEMATICAL CONTROL AND RELATED FIELDS
ISSN2156-8472
Volume8Issue:2Pages:451-473
AbstractIn this paper, we study the generalized mean-field stochastic control problem when the usual stochastic maximum principle (SMP) is not applicable due to the singularity of the Hamiltonian function. In this case, we derive a second order SMP. We introduce the adjoint process by the generalized mean-field backward stochastic differential equation. The keys in the proofs are the expansion of the cost functional in terms of a perturbation parameter, and the use of the range theorem for vector-valued measures.
KeywordStochastic maximum principle mean-field control problem singular control Frechet derivative range theorem of vector-valued measures
DOI10.3934/mcrf.2018018
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000444601600004
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
The Source to ArticleWOS
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Document TypeJournal article
CollectionUniversity of Macau
Recommended Citation
GB/T 7714
Guo, Hancheng,Xiong, Jie. A SECOND-ORDER STOCHASTIC MAXIMUM PRINCIPLE FOR GENERALIZED MEAN-FIELD SINGULAR CONTROL PROBLEM[J]. MATHEMATICAL CONTROL AND RELATED FIELDS,2018,8(2):451-473.
APA Guo, Hancheng,&Xiong, Jie.(2018).A SECOND-ORDER STOCHASTIC MAXIMUM PRINCIPLE FOR GENERALIZED MEAN-FIELD SINGULAR CONTROL PROBLEM.MATHEMATICAL CONTROL AND RELATED FIELDS,8(2),451-473.
MLA Guo, Hancheng,et al."A SECOND-ORDER STOCHASTIC MAXIMUM PRINCIPLE FOR GENERALIZED MEAN-FIELD SINGULAR CONTROL PROBLEM".MATHEMATICAL CONTROL AND RELATED FIELDS 8.2(2018):451-473.
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