Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost
Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost
复制标题
随机控制和微分博弈以及控制对动力学和运行成本的路径依赖影响
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Y. Saporito
中科院分区：
文献类型：
--
作者：
Y. Saporito
在本文中，我们考虑功能性Ito微积分框架，以找到Hamilton—Jacobi-Bellman方程的路径依赖版本，该方程具有依赖于控制路径的动态和运行成本的随机控制问题。我们还证明了这类问题的一个动态规划原理。我们将我们的结果应用于延迟类型的路径依赖。在此背景下，我们进一步研究了随机微分对策。
In this paper we consider the functional Ito calculus framework to find a path-dependent version of the Hamilton--Jacobi-Bellman equation for stochastic control problems that feature dynamics and running costs that depend on the path of the control. We also prove a dynamic programming principle for such problems. We apply our results to path-dependence of the delay type. We further study stochastic differential games in this context.