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A Stochastic Maximum Principle for Markov Chains of Mean-Field Type

Author

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  • Salah Eddine Choutri

    (Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden)

  • Tembine Hamidou

    (Learning and Game Theory Laboratory, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, UAE)

Abstract

We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications.

Suggested Citation

  • Salah Eddine Choutri & Tembine Hamidou, 2018. "A Stochastic Maximum Principle for Markov Chains of Mean-Field Type," Games, MDPI, vol. 9(4), pages 1-21, October.
    • Handle: RePEc:gam:jgames:v:9:y:2018:i:4:p:84-:d:177231
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    References listed on IDEAS

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    1. Feng, S. & Zheng, X., 1992. "Solutions of a class of nonlinear master equations," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 65-84, November.
    2. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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