论文标题
随机最佳控制问题与开放和闭环控制的不等式
Non-Equivalence of Stochastic Optimal Control Problems with Open and Closed Loop Controls
论文作者
论文摘要
对于ITô类型随机微分方程的最佳控制问题，可以将控制过程视为开环或闭环形式。在标准文献中，提供了适当的规律性，这两种类型的控件下的值函数是相等的，并且是相应（路径依赖性）HJB方程的唯一（粘度）解决方案。在此简短说明中，我们在路径依赖性设置中提供了反例，表明这些值函数一般可以不同。
For an optimal control problem of an Itô's type stochastic differential equation, the control process could be taken as open-loop or closed-loop forms. In the standard literature, provided appropriate regularity, the value functions under these two types of controls are equal and are the unique (viscosity) solution to the corresponding (path-dependent) HJB equation. In this short note, we provide a counterexample in the path dependent setting showing that these value functions can be different in general.
