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Pareto Optimal Cooperative Control of Mean-Field Backward Stochastic Differential System in Finite Horizon

Author

Listed:
  • G. Saranya

    (The Gandhigram Rural Institute (Deemed to be University))

  • R. Deepa

    (Panimalar Engineering College)

  • P. Muthukumar

    (The Gandhigram Rural Institute (Deemed to be University))

Abstract

This research article aims to investigate a new type of Pareto cooperative differential game governed by backward stochastic differential equations of mean-field type. By the characterization of Pareto optimal solutions, the proposed Pareto game problem is converted into a set of optimal control problems with single weighted objective function which is constrained by mean-field backward stochastic differential equations. First, we derive the necessary conditions for Pareto optimality of the proposed system in finite time horizon. Next, the sufficient conditions are established with the conclusion that the necessary conditions are sufficient under some convexity assumptions. Finally, for the better understanding of theoretical results, we discuss the linear quadratic optimal control problem and a mathematical transportation problem.

Suggested Citation

  • G. Saranya & R. Deepa & P. Muthukumar, 2025. "Pareto Optimal Cooperative Control of Mean-Field Backward Stochastic Differential System in Finite Horizon," Dynamic Games and Applications, Springer, vol. 15(1), pages 279-305, March.
    • Handle: RePEc:spr:dyngam:v:15:y:2025:i:1:d:10.1007_s13235-024-00566-7
    DOI: 10.1007/s13235-024-00566-7
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    References listed on IDEAS

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    1. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.
    2. Francesco Cordoni & Luca Di Persio, 2014. "Backward Stochastic Differential Equations Approach to Hedging, Option Pricing, and Insurance Problems," International Journal of Stochastic Analysis, Hindawi, vol. 2014, pages 1-11, September.
    3. Said Hamadène & Rui Mu, 2021. "Risk-Sensitive Nonzero-Sum Stochastic Differential Game with Unbounded Coefficients," Dynamic Games and Applications, Springer, vol. 11(1), pages 84-108, March.
    4. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    5. Yumo Zhang, 2022. "Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate," Annals of Finance, Springer, vol. 18(4), pages 511-544, December.
    6. Tianyang Nie & Falei Wang & Zhiyong Yu, 2022. "Maximum Principle for General Partial Information Nonzero Sum Stochastic Differential Games and Applications," Dynamic Games and Applications, Springer, vol. 12(2), pages 608-631, June.
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