论文标题
二阶路径依赖性汉密尔顿 - 雅各比 - 贝尔曼方程和应用的粘度解决方案
Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations and Applications
论文作者
论文摘要
在本文中，引入了二阶路径依赖性汉密尔顿 - 雅各比 - 贝尔曼（PHJB）方程的粘度解决方案的概念。我们将最佳控制问题的价值功能视为相关PHJB方程的唯一粘度解决方案。我们还表明，我们的粘度解决方案概念与经典解决方案的相应概念一致，并满足稳定性。还给出了向后的随机汉密尔顿 - 雅各比 - 贝尔曼方程。
In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property. Applications to backward stochastic Hamilton-Jacobi-Bellman equations are also given.
