Open AccessFree boundary problem for an optimal investment problem with a borrowing constraint
Author(s) -
Chonghu Guan,
Xun Li,
Rui Zhou,
Wen-Xin Zhou
Publication year - 2022
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.