一类带停时的奇异型随机控制模型的推广

A Class of Extended Singular Stochastic Models 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.在原模型状态过程的基础上添加了漂移因子,并将扩散因子由1推广为一个正常数σ,分退化和非退化两种情况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.通过算例,验证了变分方程的解即为最优费用函数.

By stochastic analysis method and optimal control theory, the paper discusses a class of singular stochastic control problems with stopping time, introduces a drift parameter into the state and extends the diffusion parameter from 1 to σ. The solution of the variational inequation, together with the optimal strategies are given, i.e. the optimal time. The algorithm also shows that solution is just the optimal control and the cost function. optimal stopping