基于带停时的奇异型随机控制问题的投资决策模型

Investment Model based on Singular Stochastic Control Problems with Stopping Time

研究以带停时的奇异型随机控制模型为基础的投资决策问题。为了得到最优投资策略,利用最优随机控制问题的研究方法和结论以及随机分析相关理论,通过求解一组变分不等式,得到投资决策中的最优停止时间,以及最优费用函数的解析表达式。最后,考虑投资决策中同时具有开始时间和停止时间的情况,提出相应的解决方法和思路。

This paper discusses the problem of investment decision,and the investment model is based on a class of singular stochastic control problems with stopping time.To obtain the optimal investment strategy,we use the results of optimal control problems and the theory of stochastic analysis.By solving some variational inequalities,we obtain the optimal stopping time and the analysis.By solving some variational inequalities,we obtain the optimal stopping time and the closed-form of the optimal cost function.We further consider the investment model with starting time as well as stopping time,and improve some methods and ideas to solve the model.