A Two-Person Zero-Sum Game Approach for a Retirement Decision with Borrowing Constraints

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-11 DOI:10.1137/22m1528124

Junkee Jeon, Hyeng Keun Koo, Minsuk Kwak

引用次数: 0

Abstract

SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 883-930, September 2024.
Abstract. We study an optimal consumption, investment, and retirement decision of an economic agent with borrowing constraints under a general class of utility functions. We transform the problem into a dual two-person zero-sum game, which involves two players: a stopper who is a maximizer and chooses a stopping time and a controller who is a minimizer and chooses a nonincreasing process. We derive the Hamilton–Jacobi–Bellman quasi-variational inequality (HJBQVI) of a max-min type from the dual two-person zero-sum game. We provide a solution to the HJBQVI and verify that the solution to the HJBQVI is the value of the dual two-person zero-sum game. We establish the duality result which allows us to derive the optimal strategies and value function of the primal problem from those of the dual problem. We provide examples for a class of utility functions.

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借款约束下退休决策的双人零和博弈法

SIAM 金融数学期刊》，第 15 卷第 3 期，第 883-930 页，2024 年 9 月。摘要。我们研究了一类效用函数下有借贷约束的经济主体的最优消费、投资和退休决策。我们将该问题转化为二元双人零和博弈，其中涉及两个参与者：一个是最大化并选择停止时间的停止者，另一个是最小化并选择非递增过程的控制者。我们从双人零和博弈中推导出最大最小类型的汉密尔顿-雅各比-贝尔曼准变分不等式（HJBQVI）。我们提供了 HJBQVI 的解，并验证了 HJBQVI 的解就是对偶两人零和博弈的值。我们建立了对偶性结果，从而可以从对偶问题中推导出原始问题的最优策略和价值函数。我们提供了一类效用函数的示例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.