Optimal investment problem with delay under partial information

Shuaiqi Zhang, ,School of Mathematics, China University of Mining and Technology, Jiangsu 221116, China, Jie Xiong, Xin Zhang, ,Department of Mathematics, Southern University of Science and Technology, Shenzhen, China, ,School of Mathematics, Southeast University, Nanjing, China
2019 Mathematical Control and Related Fields  
In this paper, we investigate the optimal investment problem in the presence of delay under partial information. We assume that the financial market consists of one risk free asset (bond) and one risky asset (stock) and only the price of the risky asset can be observed from the financial market. The objective of the investor is to maximize the expected utility of the terminal wealth and average of the path segment. By using the filtering theory, we establish the separation principle and reduce
more » ... inciple and reduce the problem to the complete information case. Explicit expressions for the value function and the corresponding optimal strategy are obtained by solving the corresponding Hamilton-Jacobi-Bellman equation. Furthermore, we study the sensitivity of the optimal investment strategy on the model parameters in a numerical section and both of the full and partial information schemes are simulated and compared. 2010 Mathematics Subject Classification. Primary: 49L20, 37N40; Secondary: 93E11.
doi:10.3934/mcrf.2020001 fatcat:mvmd6ijjfzhkziyhodpltt3fpa