研究了一个部分信息下的倒向随机系统的最优控制问题. 系统状态是一个线性倒向随机微分时滞方程,而容许控制适应于一个子~$\sigma$-域流, 其由多维布朗运动的分量生成. 文章引入时间超前的正向随机微分方程作为对偶过程, 借助于正倒向方程之间的对偶关系以及价值泛函导数的直接计算, 得到最优控制满足的一个必要条件. 此外, 用一个实例来阐述理论结果的应用.

In this paper, we study a control problem of backward stochastic delay system under partial information. The system state is described as a linear backward stochastic differential delay equation, and the admissible controls are adapted to a sub-filtration generated by the component of Brownian motion. A kind of time-anticipated stochastic differential equations is introduced as the adjoint process. By means of the dual method and a direct calculation of the derivative of the cost functional, we establish a necessary condition of the optimality. Moreover, we use an example to illustrate the theoretical result.