论文标题
延迟随机递归的最佳控制问题和HJB方程的动态编程原理与非lipschitz Generator
Dynamic programming principle for delayed stochastic recursive optimal control problem and HJB equation with non-Lipschitz generator
论文作者
论文摘要
在本文中，我们研究了非lipschitz发电机的延迟随机递归最佳控制问题，其中控制系统的动力学和递归成本功能都取决于状态过程的过去路径，以一般形式的形式。首先，获得了此控制问题的动态编程原理。然后，通过向后的随机微分方程的广义比较定理以及粘度解决方案的稳定性，我们在相关的汉密尔顿 - 雅各布 - 贝尔曼方程的值函数与粘度解之间建立了联系。最后，提出了在延迟的连续时间爱泼斯坦 - Zin实用程序中使用非lipschitz发电机的延迟连续时代Zin实用程序的应用。
In this paper, we study the delayed stochastic recursive optimal control problem with a non-Lipschitz generator, in which both the dynamics of the control system and the recursive cost functional depend on the past path segment of the state process in a general form. First, the dynamic programming principle for this control problem is obtained. Then, by the generalized comparison theorem of backward stochastic differential equations and the stability of viscosity solutions, we establish the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Finally, an application to the consumption-investment problem under the delayed continuous-time Epstein-Zin utility with a non-Lipschitz generator is presented.
