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Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay

Author

Listed:
  • Han, Yuecai
  • Li, Yuhang
  • Li, Zheng

Abstract

In this paper, motivated by optimal control problem with time-varying delay, we study a type of generalized forward–backward stochastic differential equation. Both delay and anticipated terms appear in both forward equation and backward equation. The existence and uniqueness of the solution is obtained. As an application, the linear quadratic optimal control problem, where both state process and control process contain time-varying delay, is solved.

Suggested Citation

  • Han, Yuecai & Li, Yuhang & Li, Zheng, 2025. "Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay," Statistics & Probability Letters, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:stapro:v:223:y:2025:i:c:s0167715225000598
    DOI: 10.1016/j.spl.2025.110414
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