带停时的奇异型随机控制问题在金融投资模型中的应用

The Problem of Singular Stochastic Control with Stopping Time Applied in the Investment Models

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问题在金融投资模型中的应用,将该带停时的奇异型随机控制模型的受控状态过程和费用函数结构都推广到了最一般的形式,使该模型的应用范围更加广泛.通过讨论一组相应的变分不等式的解,分别对退化和非退化两种情况给出了此随机控制问题的最优策略,相应得出了投资模型中的最佳决策,并且证明了变分不等式的解即为最优费用函数.与以往不同的是,所得的相关结论应用到了金融投资模型中,从而解决了一类金融投资问题.

By stochastic analysis method and the optimal control theory, this paper discusses a class of singular stochastic control problems with stopping time applied in the investment models. The model of singular stochastic control is extended into general case, and the paper gives the solution of the variational inequalities , and gives the optimal strategies, that is the optimal strategy in the investment models. It also shows the solution is just the optimal cost function.