A Framework for the Dynamic Programming Principle and Martingale-Generated Control Correspondences
A Framework for the Dynamic Programming Principle and Martingale-Generated Control Correspondences
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动态规划原理和鞅生成的控制对应关系的框架
DOI：
10.1007/s00245-019-09589-8
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发表时间：
2019
影响因子：
1.8
通讯作者：
Žitković, Gordan
中科院分区：
文献类型：
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作者：
Fayvisovich, Roman;Žitković, Gordan
我们构建了一个抽象的框架，其中的动态规划原理（DPP）可以很容易地证明。它包含了广泛的常见的随机控制问题的弱制定，并处理问题的“鞅制定”特别容易。我们给出两个例子;首先，我们建立了一般控制扩散的DPP，并证明了在极小条件下，它们的值函数是相应的Hamilton-Jacobi-Bellman方程的粘性解。之后，我们展示了如何处理奇异控制的经典单调跟随器问题的例子。
We construct an abstract framework in which the dynamic programming principle (DPP) can be readily proven. It encompasses a broad range of common stochastic control problems in the weak formulation, and deals with problems in the “martingale formulation” with particular ease. We give two illustrations; first, we establish the DPP for general controlled diffusions and show that their value functions are viscosity solutions of the associated Hamilton–Jacobi–Bellman equations under minimal conditions. After that, we show how to treat singular control on the example of the classical monotone-follower problem.