# American Institute of Mathematical Sciences

June  2020, 10(2): 365-378. doi: 10.3934/mcrf.2020001

## Optimal investment problem with delay under partial information

 1 School of Mathematics, China University of Mining and Technology, Jiangsu 221116, China 2 Department of Mathematics, Southern University of Science and Technology, Shenzhen, China 3 School of Mathematics, Southeast University, Nanjing, China

* Corresponding author: Shuaiqi Zhang

Received  July 2018 Revised  December 2018 Published  November 2019

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 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.

Citation: Shuaiqi Zhang, Jie Xiong, Xin Zhang. Optimal investment problem with delay under partial information. Mathematical Control & Related Fields, 2020, 10 (2) : 365-378. doi: 10.3934/mcrf.2020001
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##### References:
Comparison of $\hat\mu$
Comparison of $v$
Comparison of $V$
Comparison of $v$
Comparison of $V$
Comparison of $\hat\mu$
Comparison of $v$
Comparison of $V$
Comparison of $V$ and $\bar V$
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