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Stochastic Maximum Principle for Partially Observed Optimal Control Problems of General McKean–Vlasov Differential Equations

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Abstract

The paper studies partially observed optimal control problems of general McKean–Vlasov differential equations, in which the coefficients depend on the state of the solution process as well as of its law and the control variable. By applying Girsanov’s theorem with a standard variational technique, we establish a stochastic maximum principle on the assumption that the control domain is convex. As an application, partially observed linear-quadratic control problem is discussed.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript considerably. The first author was supported by Algerian PRFU project Grant C00L03UN070120190003. The second and third authors were supported by Algerian PRFU project Grant C00L03UN070120180003.

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Authors and Affiliations

  1. Laboratory of Applied Mathematics, University of Biskra, Box 145, 07000, Biskra, Algeria

    Imad Eddine Lakhdari

  2. Laboratory of Applied Mathematics, University Mohamed Khider, Biskra, Po. Box 145, 07000, Biskra, Algeria

    Hakima Miloudi

  3. Department of Mathematics, University Mohamed khider, Biskra, Po. Box 145, 7000, Biskra, Algeria

    Mokhtar Hafayed

Authors
  1. Imad Eddine Lakhdari
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  2. Hakima Miloudi
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  3. Mokhtar Hafayed
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Correspondence to Imad Eddine Lakhdari.

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Communicated by Sohrab Effati.

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Lakhdari, I.E., Miloudi, H. & Hafayed, M. Stochastic Maximum Principle for Partially Observed Optimal Control Problems of General McKean–Vlasov Differential Equations. Bull. Iran. Math. Soc. 47, 1021–1043 (2021). https://doi.org/10.1007/s41980-020-00426-1

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  • DOI: https://doi.org/10.1007/s41980-020-00426-1

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