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

Author

Listed:
  • Mokhtar Hafayed

    (Biskra University)

  • Syed Abbas

    (School of Basic Sciences, Indian Institute of Technology)

  • Abdelmadjid Abba

    (Biskra University)

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.

Suggested Citation

  • Mokhtar Hafayed & Syed Abbas & Abdelmadjid Abba, 2015. "On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Lévy Processes," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1051-1069, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-015-0762-4
    DOI: 10.1007/s10957-015-0762-4
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    References listed on IDEAS

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    1. Mokhtar Hafayed & Syed Abbas, 2014. "On Near-Optimal Mean-Field Stochastic Singular Controls: Necessary and Sufficient Conditions for Near-Optimality," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 778-808, March.
    2. Mitsui, Ken-ichi & Tabata, Yoshio, 2008. "A stochastic linear-quadratic problem with Lévy processes and its application to finance," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 120-152, January.
    3. 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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    Cited by:

    1. Alain Bensoussan & Boualem Djehiche & Hamidou Tembine & Sheung Chi Phillip Yam, 2020. "Mean-Field-Type Games with Jump and Regime Switching," Dynamic Games and Applications, Springer, vol. 10(1), pages 19-57, March.

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