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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.
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    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.
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    6. 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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