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A general characterization of the stochastic optimal combined control of mean field stochastic systems with application

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Abstract

In this paper, a general characterization of the optimal stochastic combined control for mean-field jump-systems is derived by applying mixed convex-spike perturbation method. The diffusion coefficient depends on the continuous control variable and the control domain is not necessary convex. In our combined mean-field control problem, we discuss two classes of jumps for the state processes, the inaccessible jumps which caused by Poisson martingale measure and the predictable ones which caused by the singularity of the control variable. Markowitz’s mean–variance portfolio selection problem with intervention control is discussed.

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Acknowledgements

The authors would like to thank, the associate editor, and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript considerably. This work was supported by the Tubitak project (Grant 2221), Turkey.

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Authors and Affiliations

  1. Department of Mathematics, Yasar University, University aven, Agaclı Yol No. 35-57, Izmir, Turkey

    Shahlar Meherrem, Deniz H. Gucoglu & Saban Eren

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

    Mokhtar Hafayed

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  1. Shahlar Meherrem
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  2. Mokhtar Hafayed
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  3. Deniz H. Gucoglu
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  4. Saban Eren
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Correspondence to Shahlar Meherrem.

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Meherrem, S., Hafayed, M., Gucoglu, D.H. et al. A general characterization of the stochastic optimal combined control of mean field stochastic systems with application. Int. J. Dynam. Control 6, 873–880 (2018). https://doi.org/10.1007/s40435-017-0323-9

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  • DOI: https://doi.org/10.1007/s40435-017-0323-9

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