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

Chonghu Guan | Zendy; Xun Li | Zendy; Rui Zhou | Zendy; Wenxin Zhou | Zendy

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

Author(s) -

Chonghu Guan,

Xun Li,

Rui Zhou,

Wenxin Zhou

Publication year - 2021

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2021049

Subject(s) - constraint (computer aided design) , free boundary problem , uniqueness , boundary value problem , boundary (topology) , mathematics , investment (military) , mathematical optimization , nonlinear system , mathematical analysis , mathematical economics , geometry , physics , law , quantum mechanics , politics , political science

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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