A new method to solve the Hamilton-Jacobi-Bellman equation for a stochastic portfolio optimization model with boundary memory

Xuhui Wang; Lei Hu

doi:10.3934/jimo.2021137

Article Contents

2022, Volume 18, Issue 6: 3831-3845. Doi: 10.3934/jimo.2021137

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A new method to solve the Hamilton-Jacobi-Bellman equation for a stochastic portfolio optimization model with boundary memory

Xuhui Wang^1, and
Lei Hu^2, ,

1.
Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, 1 Shi-Zi Street, Suzhou 215000, China
2.
School of Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai 200433, China

^* Corresponding author: Lei Hu
^* Corresponding author: Lei Hu

Received: January 2021

Revised: April 2021

Early access: August 2021

Published: September 2022

The work is supported by NSF grant No.11871435

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Abstract

Portfolio optimization problem with memory effect, namely, taking the past performance of portfolio into account, which is motivated by the fact that the decisions of the investors are influenced by the historic performance of the portfolio, has recently been of interest to researchers. Due to the memory effect, this type of problem is challenging. The main purpose of this paper is to propose a new approach to solve the Hamilton-Jacobi-Bellman (HJB) equation for the stochastic portfolio optimization model, which is more simple and generalized. We study the portfolio management problem under single investor and multi-investor framework. We establish certain conditions under which the problem can be reduced to the classical stochastic control problem and give some examples to show the advantages of our approach.

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Mathematics Subject Classification: Primary: 60H15, 60J65; Secondary: 91A06.

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References

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