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<p>In this article, the authors propose an innovative life-cycle planning model with behavioral considerations in a realistic financial market. Specifically, the wage earner invests in one risk-free asset and one risky asset whose price dynamics follow the constant elasticity of variance (CEV) model. The performance functional of the wage earner is defined as maximizing the expected utility derived from the intertemporal consumption, bequest, and terminal wealth across an uncertain lifespan. Hyperbolic absolute risk aversion (HARA) utility preference is considered because it is more general and encompasses the commonly used power utility, logarithmic utility, and exponential utility as special cases. Applying the dynamic programming principle and the Legendre transform-dual approach, the authors have derived explicit formulae for optimal investment, consumption and life insurance purchase decisions and the value function. Numerical demonstration has also been provided to illustrate the influence of several momentous parameters on the optimal strategies.</p>

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Life-Cycle Decision Model with HARA Preference and CEV Model

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Hao Wang,
  • Erqing Huang,
  • Lin Xu,
  • Ning Wang

摘要

In this article, the authors propose an innovative life-cycle planning model with behavioral considerations in a realistic financial market. Specifically, the wage earner invests in one risk-free asset and one risky asset whose price dynamics follow the constant elasticity of variance (CEV) model. The performance functional of the wage earner is defined as maximizing the expected utility derived from the intertemporal consumption, bequest, and terminal wealth across an uncertain lifespan. Hyperbolic absolute risk aversion (HARA) utility preference is considered because it is more general and encompasses the commonly used power utility, logarithmic utility, and exponential utility as special cases. Applying the dynamic programming principle and the Legendre transform-dual approach, the authors have derived explicit formulae for optimal investment, consumption and life insurance purchase decisions and the value function. Numerical demonstration has also been provided to illustrate the influence of several momentous parameters on the optimal strategies.