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On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Lévy Processes

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Abstract

In this paper, we study the mean-field-type partial information stochastic optimal control problem, where the system is governed by a controlled stochastic differential equation, driven by the Teugels martingales associated with some Lévy processes and an independent Brownian motion. We derive necessary and sufficient conditions of the optimal control for these mean-field models in the form of a maximum principle. The control domain is assumed to be convex. As an application, the partial information linear quadratic control problem of the mean-field type is discussed.

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Acknowledgments

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 CNEPRU Project Grant B01420130137, 2014-2016.

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Authors and Affiliations

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

    Mokhtar Hafayed

  2. School of Basic Sciences, Indian Institute of Technology, Mandi, 175001, H.P., India

    Syed Abbas

  3. Department of Mathematics, Biskra University, PO. Box 145, 07000, Biskra, Algeria

    Abdelmadjid Abba

Authors
  1. Mokhtar Hafayed
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  2. Syed Abbas
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  3. Abdelmadjid Abba
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Correspondence to Abdelmadjid Abba.

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Hafayed, M., Abbas, S. & Abba, A. On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Lévy Processes. J Optim Theory Appl 167, 1051–1069 (2015). https://doi.org/10.1007/s10957-015-0762-4

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  • DOI: https://doi.org/10.1007/s10957-015-0762-4

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