Affiliations: [a] School of Science, Nanjing Forestry University, Nanjing, Jiangsu, China
| [b]
School of Management and Engineering, Nanjing University, Nanjing, Jiangsu, China
| [c] School of Mathematics and Stochastics, Nanjing University of Science and Technology, Nanjing, Jiangsu, China
| [d]
School of Mathematics and Statistics, Nanjing University of Information Science and Techology, Nanjing, Jiangsu, China
| [e]
Department of Community Health Sciences, University of Manitoba, Bannatyne Ave, Winnipeg, Canada
Correspondence:
[*]
Corresponding author. Yuanguo Zhu, School of Mathematics and Stochastics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China. E-mail: ygzhu@njust.edu.cn..
Abstract: This paper discusses an uncertain time optimal control problem by considering time efficiency, which is to optimize the objective function about the first hitting time subject to uncertain differential equations. According to the definition of the α-path, the uncertain time optimal control problem is transformed into an equivalent deterministic optimal control problem. Two kinds of time optimal control models are presented where optimistic value and reaching index are chosen as the optimality criteria, respectively. Applying the proposed uncertain optimal control model to a portfolio selection problem, we obtain the uncertainty distribution of the first hitting time (the investors’ first profit time). Meanwhile, sufficient conditions of the optimal control strategy of such models are provided. Numerical simulations are provided which reveal the change for our optimal control strategy.
Keywords: Uncertainty optimal control, first
hitting time, portfolio selection, optimistic value, reaching index
