带有损失规避和过去最大消费参考的最优消费

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-15 DOI:10.1137/22m149212x

Xun Li, Xiang Yu, Qinyi Zhang

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引用次数: 0

摘要

SIAM 金融数学期刊》，第 15 卷第 1 期，第 121-160 页，2024 年 3 月。摘要本文研究了一个损失规避代理的最优消费问题，该问题参考了过去的消费最大值。为了考虑相对消费的损失规避，本文采用了一种 S 型效用，即衡量非负消费率与历史消费峰值的一部分之间的差额。我们考虑的是效用相对于消费的凹包络，这使得我们可以将注意力集中在一个辅助的 HJB 变式不等式上，即凹化原理和动态编程论证的强度。通过应用对偶变换和平稳拟合条件，辅助 HJB 变不等式以片断封闭形式求解，并得到财富变量的一些临界值。最优消费和投资控制可以以片断反馈形式得到。提供了关于最优性和凹化原理的严格验证证明。此外，还给出了一些数值敏感性分析和财务影响。

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Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum

SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 121-160, March 2024.
Abstract. This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the nonnegative consumption rate and a fraction of the historical spending peak. We consider the concave envelope of the utility with respect to consumption, allowing us to focus on an auxiliary HJB variational inequality on the strength of concavification principle and dynamic programming arguments. By applying the dual-transform and smooth-fit conditions, the auxiliary HJB variational inequality is solved in piecewise closed form, and some thresholds of the wealth variable are obtained. The optimal consumption and investment control can be derived in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Some numerical sensitivity analysis and financial implications are also presented.

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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.