This paper investigates the optimal control problem arising in advertising model with delay. The authors reformulate the problem in Hilbert space by stochastic evolution equation and consider the optimal control problem of controlled stochastic evolution system. The necessary and sufficient optimality conditions of the control are established. The proposed approach is different from most existing studies of optimal advertising policy problem with delay. These results are applied to the optimal advertising policy problem under two different structures and the optimal advertising strategies are obtained.

中文翻译：

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时滞广告模型中的随机最优控制问题

本文研究时滞广告模型中的最优控制问题。作者通过随机演化方程重新构造了希尔伯特空间中的问题，并考虑了受控随机演化系统的最优控制问题。建立了控制的必要和充分的最优条件。所提出的方法与大多数现有的关于最优广告政策问题的研究有所不同。将这些结果应用于两种不同结构下的最优广告策略问题，得到了最优广告策略。