This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical space at each time t . Motivated by some financial applications, we show that several types of dynamic trading constraints can be reformulated into expectation constraints on paths of controlled state processes. Our results can therefore be employed to recover the dynamic programming principle for these optimal investment problems under dynamic constraints, possibly path-dependent, in a non-Markovian framework.

中文翻译：

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期望约束下随机控制的动态规划原理

本文研究了使用可测选择方法对连续过程进行随机控制的动态规划原理。这项工作的新颖之处在于在每个时间 t 将中间期望约束纳入规范空间。受一些金融应用的启发，我们展示了几种类型的动态交易约束可以重新表述为对受控状态过程路径的期望约束。因此，我们的结果可用于在非马尔可夫框架中在动态约束下恢复这些最优投资问题的动态规划原理，可能是路径相关的。