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Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach

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  • Olivier Menoukeu Pamen

    (University of Liverpool)

Abstract

In this paper, we study a robust recursive utility maximization problem for time-delayed stochastic differential equation with jumps. This problem can be written as a stochastic delayed differential game. We suggest a maximum principle of this problem and obtain necessary and sufficient condition of optimality. We apply the result to study a problem of consumption choice optimization under model uncertainty.

Suggested Citation

  • Olivier Menoukeu Pamen, 2015. "Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 998-1031, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-013-0484-4
    DOI: 10.1007/s10957-013-0484-4
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    References listed on IDEAS

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    Cited by:

    1. Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers," Papers 1705.02440, arXiv.org, revised Jul 2018.
    2. Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers," CARF F-Series CARF-F-409, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Olivier Menoukeu-Pamen & Romuald Hervé Momeya, 2017. "A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 349-388, June.
    4. Tiago Roux Oliveira & Victor Hugo Pereira Rodrigues & Miroslav Krstić & Tamer Başar, 2021. "Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 700-735, December.
    5. Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and Quadratic-Exponential Growth Drivers," CIRJE F-Series CIRJE-F-1047, CIRJE, Faculty of Economics, University of Tokyo.
    6. Rodwell Kufakunesu & Calisto Guambe, 2018. "On the optimal investment-consumption and life insurance selection problem with an external stochastic factor," Papers 1808.04608, arXiv.org.
    7. Masaaki Fujii & Akihiko Takahashi, 2018. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers (Revised version of F-409)," CARF F-Series CARF-F-431, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Rodwell Kufakunesu & Calisto Guambe & Lesedi Mabitsela, 2018. "Risk-based optimal portfolio of an insurer with regime switching and noisy memory," Papers 1808.04604, arXiv.org, revised Mar 2019.
    9. Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and Quadratic-Exponential Growth Drivers," CIRJE F-Series CIRJE-F-1047, CIRJE, Faculty of Economics, University of Tokyo.

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