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Pareto Game of Stochastic Differential System with Terminal State Constraint

Author

Listed:
  • Pengyan Huang

    (Shandong University
    Shandong University of Finance and Economics)

  • Guangchen Wang

    (Shandong University)

  • Shujun Wang

    (Shandong University)

Abstract

In this paper, we focus on a type of Pareto game of stochastic differential equation with terminal state constraint. Firstly, we transform equivalently a nonlinear Pareto game problem with convex control space and terminal state constraint into a constrained stochastic optimal control problem. By virtue of duality theory and stochastic maximum principle, a necessary condition for Pareto efficient strategy is established. With some convex assumptions, we also give a sufficient condition for Pareto efficient strategy. Secondly, we consider a linear-quadratic Pareto game with terminal state constraint, and a feedback representation for Pareto efficient strategy is derived. Finally, as an application, we solve a government debt stabilization problem and give some numerical results.

Suggested Citation

  • Pengyan Huang & Guangchen Wang & Shujun Wang, 2025. "Pareto Game of Stochastic Differential System with Terminal State Constraint," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-30, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02612-9
    DOI: 10.1007/s10957-025-02612-9
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