This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation is derived for the optimal control, which is a linear feedback of the entire past history and the expected value of the future state trajectory in a short period of time. To obtain the optimal feedback, a new class of delayed Riccati equations and delayed-advanced forward-backward stochastic differential equations are introduced. Furthermore, the unique solvability of their solutions are discussed in detail.

中文翻译：

---

时滞倒向随机微分方程的线性二次最优控制问题

本文关注的是时滞后向随机微分方程的线性二次最优控制问题。为最佳控制导出了一个明确的表示形式，它是整个过去历史和未来状态轨迹的期望值在短时间内的线性反馈。为了获得最佳反馈，引入了一类新的时滞Riccati方程和时滞先进的前向-后向随机微分方程。此外，详细讨论了其解决方案的独特可解性。