A double obstacle problem in an optimal investment problem. (July 2023)

• Record Type: Journal Article
• Authors: Kim, Takwon; Lee, Ki-Ahm; Park, Jinwan
• Is Part Of: Nonlinear analysis. Volume 232(2023)
• Publication Date: 2023-07
• Subjects: Obstacle problem -- Double obstacle problem -- Free boundary problem -- Optimal investment problem -- CEV model; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2023.113282
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study a double obstacle problem in partial differential equation that arises in an optimization problem in finance. Precisely, we consider the double obstacle problem which is related to the optimal investment problem with proportional transaction costs of an investor with the logarithmic utility in finite time under the constant elasticity of variance (CEV) model. First, we construct a solution of the double obstacle problem and prove the monotonicity of its free boundaries. From the solution to the double obstacle problem, we construct the solution of the optimization problem. Hence, our result regarding monotonicity indicates the optimal strategy for the optimization problem.