Free boundary problem for an optimal investment problem with a borrowing constraint

Chonghu Guan; Xun Li; Rui Zhou; Wenxin Zhou

doi:10.3934/jimo.2021049

Free boundary problem for an optimal investment problem with a borrowing constraint

Chonghu Guan, Xun Li, Rui Zhou, Wenxin Zhou

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small.

Original language	English
Pages (from-to)	1915-1934
Number of pages	20
Journal	Journal of Industrial and Management Optimization
Volume	18
Issue number	3
DOIs	https://doi.org/10.3934/jimo.2021049
Publication status	Published - May 2022

Keywords

borrowing constraint
CRRA utility
Free boundary problem
optimal investment
stochastic optimal control

ASJC Scopus subject areas

Business and International Management
Strategy and Management
Control and Optimization
Applied Mathematics

More information

10.3934/jimo.2021049

http://hdl.handle.net/10397/93822

Cite this

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title = "Free boundary problem for an optimal investment problem with a borrowing constraint",

abstract = "This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small.",

keywords = "borrowing constraint, CRRA utility, Free boundary problem, optimal investment, stochastic optimal control",

author = "Chonghu Guan and Xun Li and Rui Zhou and Wenxin Zhou",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary: 91B70, 91G10; Secondary: 35R35, 35B65. Key words and phrases. Free boundary problem, stochastic optimal control, optimal investment, CRRA utility, borrowing constraint. The work is supported by NNSF of China (No.11901244 and No.11901093), Universities and Colleges Special Innovation Project of Guangdong Province (No.2019KTSCX166), and Research Grants Council of Hong kong under grant 15213218 and 15215319. ∗ Corresponding author: Rui Zhou. Publisher Copyright: {\textcopyright} 2022. All Rights Reserved.",

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AU - Zhou, Wenxin

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N2 - This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small.

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Free boundary problem for an optimal investment problem with a borrowing constraint

Abstract

Keywords

ASJC Scopus subject areas

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