Optimal investment problem with delay under partial information

Zhang Shuaiqi; Xiong Jie; Zhang Xin

doi:10.3934/mcrf.2020001

Article Contents

2020, Volume 10, Issue 2: 365-378. Doi: 10.3934/mcrf.2020001

This issue Previous Article Finite element error estimates for one-dimensional elliptic optimal control by BV-functions Next Article Necessary condition for optimal control of doubly stochastic systems

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
^* Corresponding author: Shuaiqi Zhang

Received: June 30, 2018

Revised: November 30, 2018

Early access: November 2019

Published: April 2020

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 49L20, 37N40; Secondary: 93E11.

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Figure 1. Comparison of $ \hat\mu $

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Figure 2. Comparison of $ v $

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Figure 3. Comparison of $ V $

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Figure 4. Comparison of $ v $

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Figure 5. Comparison of $ V $

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Figure 6. Comparison of $ \hat\mu $

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Figure 7. Comparison of $ v $

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Figure 8. Comparison of $ V $

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Figure 9. Comparison of $ V $ and $ \bar V $

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