This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational method and a filtering technique. Also, we establish a sufficient condition without assumption of the concavity. Two examples shed light on the theoretical results are established in the paper. In particular, in the example of an optimal investment problem with delay, its numerical simulation shows the effect of delay via a discretization technique for forward-backward stochastic differential equations (FBSDEs) with delay and anticipate terms.

中文翻译：

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具有延迟的部分观测随机控制系统的随机最大值原理

本文研究了由具有延迟的随机微分方程支配的状态的部分可观测最优控制问题。我们使用变分方法和过滤技术为此类最优控制问题开发了随机最大值原理。此外，我们在不假设凹度的情况下建立了一个充分条件。本文建立了两个例子来阐明理论结果。特别是，在具有延迟的最优投资问题的示例中，其数值模拟通过具有延迟和预期项的前向后向随机微分方程 (FBSDE) 的离散化技术显示了延迟的影响。