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A Progressive Maximum Principle of Fully Coupled Mean-Field System with Jumps

Author

Listed:
  • Tian Chen

    (Suzhou Research Institute, Shandong University)

  • Hongyu Shi

    (School of Mathematics, Shandong University)

  • Zhen Wu

    (School of Mathematics, Shandong University)

Abstract

In this paper, we investigate a class of progressive optimal control problems for fully coupled mean-field forward-backward systems with random jumps. Under weakly-coupled conditions and an arbitrary fixed time horizon, we establish the well-posedness of a class of fully coupled mean-field forward-backward stochastic differential equations with jumps, ensuring the well-posedness of the state, variational and adjoint equations. Next, using the convex variational method, we provide a stochastic maximum principle for the progressive optimal control of this mean-field system. Our maximum principle is divided into two parts: a continuous component, which characterizes the optimal control during continuous periods, and a jump component, which defines the optimal control behavior at jump times. Additionally, we provide a sufficient maximum principle under certain convexity assumptions. Finally, we apply these theoretical results to a linear-quadratic control problem, obtaining both the open-loop optimal control and its corresponding feedback representation, further demonstrating the practical effectiveness of our findings.

Suggested Citation

  • Tian Chen & Hongyu Shi & Zhen Wu, 2025. "A Progressive Maximum Principle of Fully Coupled Mean-Field System with Jumps," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-28, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02760-y
    DOI: 10.1007/s10957-025-02760-y
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