Life-cycle planning with CEV model and time-inconsistent preferences

IF 4.8 2区经济学 Q1 BUSINESS, FINANCE International Review of Economics & Finance Pub Date : 2024-08-26 DOI:10.1016/j.iref.2024.103517

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Abstract

In this paper, we investigate an optimization problem for a wage earner seeking to maximize expected utilities until retirement by choosing optimal consumption, investment, and life insurance purchase strategies. The constant elasticity of variance (CEV) model is adopted to describe the price process of the risky asset. Additionally, we assume that the wage earner has time-inconsistent preferences. This makes the wage earner discount her payoff by a non-constant discount rate. Applying the dynamic programming principle, we have derived the Hamilton-Jacobi-Bellman (HJB) equation corresponding to the optimization problem. Furthermore, we present semi-analytical expressions for optimal strategies and value functions in three cases: the benchmark model with time-consistent preferences, the naive and sophisticated wage earners with time-inconsistent preferences. Finally, illustrations of the optimal solutions and some economic insights are provided in the numerical examples.

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使用 CEV 模型和时间不一致偏好进行生命周期规划

在本文中，我们研究了一个工薪族的最优化问题，即通过选择最优消费、投资和人寿保险购买策略，寻求退休前预期效用的最大化。本文采用恒定方差弹性（CEV）模型来描述风险资产的价格过程。此外，我们假定工薪阶层具有时间不一致偏好。这使得工薪族以非恒定贴现率对其收益进行贴现。应用动态编程原理，我们推导出了与优化问题相对应的汉密尔顿-雅各比-贝尔曼（HJB）方程。此外，我们还给出了三种情况下最优策略和价值函数的半解析表达式：具有时间一致性偏好的基准模型、具有时间不一致偏好的天真和复杂的工薪阶层。最后，我们通过数值示例说明了最优解和一些经济学见解。

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来源期刊

International Review of Economics & Finance Multiple-

CiteScore

7.30

自引率

2.20%

发文量

253

期刊介绍： The International Review of Economics & Finance (IREF) is a scholarly journal devoted to the publication of high quality theoretical and empirical articles in all areas of international economics, macroeconomics and financial economics. Contributions that facilitate the communications between the real and the financial sectors of the economy are of particular interest.