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中文摘要：
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σ-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.
英文摘要：
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 subfiltration 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.
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