论文标题
随机系数的随机递归控制问题的最大原理与动态编程原理之间的关系
The Relationship between Maximum Principle and Dynamic Programming Principle for Stochastic Recursive Control Problem with Random Coefficients
论文作者
论文摘要
本文旨在探讨随机系数随机递归控制问题的最大原理与动态编程原理之间的关系。在系数的某些规则条件下，获得了与随机系数的汉密尔顿系统与随机汉密尔顿 - 雅各比 - 贝尔曼方程的关系。它与确定性系数的情况大不相同，因为随机汉密尔顿 - 雅各比 - 贝尔曼方程是一个向后的随机偏微分方程，解决方案是一对随机场而不是确定性函数。基于这种关系的明确说明了一个线性二次递归效用优化问题。
This paper aims to explore the relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients. Under certain regular conditions for the coefficients, the relationship between the Hamilton system with random coefficients and stochastic Hamilton-Jacobi-Bellman equation is obtained. It is very different from the deterministic coefficients case since stochastic Hamilton-Jacobi-Bellman equation is a backward stochastic partial differential equation with solution being a pair of random fields rather than a deterministic function. A linear quadratic recursive utility optimization problem is given as an explicitly illustrated example based on this kind of relationship.
