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Stochastic Linear-Quadratic Mean-Field Games of Controls for Delayed Systems with Jump Diffusion

Author

Listed:
  • Na Li

    (Shandong University of Finance and Economics)

  • Yilin Wei

    (Shandong University of Finance and Economics)

  • Qingfeng Zhu

    (Shandong University of Finance and Economics)

Abstract

In this paper, we investigate a class of stochastic linear-quadratic (LQ) mean-field games (MFGs) for large-population (LP) systems, where the dynamic of each agent is described by a stochastic differential delayed equation with Brownian motions and Poisson jumps. Based on the MFG theory, agents are influenced by both individual and common information when formulating strategies in the stochastic LP system. Firstly, we solve the LQ-MFG of control problem for the stochastic LP system with delay and Poisson jumps by employing the stochastic Hamiltonian system. Secondly, using a separation technique, we derive an asymptotic representation of the average control term. Thirdly, we obtain an explicit representation of the decentralized optimal control for each agent in open-loop form, and in closed-loop form for a special case. Then, we rigorously prove that the set of these decentralized optimal controls constitutes an $$\epsilon $$ ϵ -Nash equilibrium. Finally, to illustrate the theoretical findings, we apply our framework to a monetary asset management problem and validate the results through numerical simulations.

Suggested Citation

  • Na Li & Yilin Wei & Qingfeng Zhu, 2025. "Stochastic Linear-Quadratic Mean-Field Games of Controls for Delayed Systems with Jump Diffusion," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-34, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02730-4
    DOI: 10.1007/s10957-025-02730-4
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