一类带停时的奇异型随机控制问题的研究

A Class of Singular Stochastic Controls with Stopping Time

以随机分析的知识和最优控制理论为基础,讨论了一类带停时的奇异型随机控制的折扣费用模型,在原模型的状态过程的基础上添加了漂移因子和扩散因子,并在λ<δα的情况下讨论了该问题相应的变分方程的解,给出了此随机控制问题的最优策略,即最优控制和最优停时,并且证明了变分方程的解即为最优费用函数.

By stochastic analysis method and the optimal control theory, this paper discusses a class of singular stochastic control problems with stopping time,and introduces a drift parameter and a diffusion parameter into the state. We give the solution of the variational inequation when it meets λ〈δα, and give the optimal strategies, that is the optimal control and the optimal stopping time. We also show the solution is just the optimal cost function.