论文标题
随机路径依赖的汉密尔顿 - 雅各比 - 贝尔曼方程和受控的随机微分方程，具有随机路径依赖性系数
Stochastic Path-Dependent Hamilton-Jacobi-Bellman Equations and Controlled Stochastic Differential Equations with Random Path-Dependent Coefficients
论文作者
论文摘要
在本文中，我们提出并研究了随机路径依赖性的汉密尔顿 - 雅各比 - 贝尔曼（SPHJB）方程，该方程自然来自具有路径依赖性和可测量随机性的随机微分方程的最佳随机控制问题。提出了粘度解决方案和经典解的概念，最佳随机控制问题的价值函数被证明是相关SPHJB方程的粘度解决方案。对于某些超差方案例，还给出了有关粘度解决方案的独特性结果，而经典解决方案的独特性则用于一般情况。此外，事实证明，在路径依赖性设置中，Itô-Kunita-Wentzell-Krylov公式用于随机场和随机微分方程的组成。
In this paper, we propose and study the stochastic path-dependent Hamilton-Jacobi-Bellman (SPHJB) equation that arises naturally from the optimal stochastic control problem of stochastic differential equations with path-dependence and measurable randomness. Both the notions of viscosity solution and classical solution are proposed, and the value function of the optimal stochastic control problem is proved to be the viscosity solution to the associated SPHJB equation. A uniqueness result about viscosity solutions is also given for certain superparabolic cases, while the uniqueness of classical solution is addressed for general cases. In addition, an Itô-Kunita-Wentzell-Krylov formula is proved for the compositions of random fields and stochastic differential equations in the path-dependent setting.
