A double obstacle problem in an optimal investment problem

被引：0

作者：

Kim, Takwon ^{[1
]}

Lee, Ki-Ahm ^{[2
,3
]}

Park, Jinwan ^{[4
]}

机构：

[1] Seoul Natl Univ, Res Inst Math, Gwanak Ro 1, Seoul 08826, South Korea

[2] Seoul Natl Univ, Dept Math Sci, Gwanak Ro 1, Seoul 08826, South Korea

[3] Seoul Natl Univ, Res Inst Math, Gwanak Ro 1, Seoul 08826, South Korea

[4] Kongju Natl Univ, Dept Appl Math, Gongju 32588, Chungcheongnam, South Korea

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 232卷

基金：

新加坡国家研究基金会;

关键词：

Obstacle problem; Double obstacle problem; Free boundary problem; Optimal investment problem; CEV model; FREE-BOUNDARY; REGULARITY; CONSUMPTION;

D O I：

10.1016/j.na.2023.113282

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. & COPY; 2023 Elsevier Ltd. All rights reserved.

引用

页数：40

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