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<p>This paper investigates an optimal control problem for fully coupled forward–backward stochastic differential equations (FBSDEs in short) driven by sub-diffusion. A stochastic maximum principle is derived for cases where the control domain is not necessarily convex and the diffusion term is independent of the control variable. Furthermore, the state-constrained problem is addressed through the application of Ekeland’s variational principle. Finally, the theoretical results are applied to a cash management optimization problem in a bear market, yielding the explicit optimal strategy.</p>

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The Optimal Control Problem of Fully Coupled FBSDEs Driven by Sub-diffusion with Applications

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Chenhui Hao,
  • Jingtao Shi,
  • Shuaiqi Zhang

摘要

This paper investigates an optimal control problem for fully coupled forward–backward stochastic differential equations (FBSDEs in short) driven by sub-diffusion. A stochastic maximum principle is derived for cases where the control domain is not necessarily convex and the diffusion term is independent of the control variable. Furthermore, the state-constrained problem is addressed through the application of Ekeland’s variational principle. Finally, the theoretical results are applied to a cash management optimization problem in a bear market, yielding the explicit optimal strategy.