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

Yuecai Han, Yuhang Li and Zheng Li

Statistics & Probability Letters, 2025, vol. 223, issue C

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.

Keywords: Forward–backward stochastic differential equations; Time-varying delay; Optimal control (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110414

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