Pareto Game of Stochastic Differential System with Terminal State Constraint

Pengyan Huang (), Guangchen Wang () and Shujun Wang ()
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Pengyan Huang: Shandong University
Guangchen Wang: Shandong University
Shujun Wang: Shandong University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 1, No 8, 30 pages

Abstract: 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.

Keywords: Cooperative differential game; Government debt stabilization; Pareto optimality; State constraint; Stochastic differential equation; 60H10; 91A12; 91A15; 93E20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02612-9

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