Abstract

This paper studies the optimal investment-consumption decision under the constant elasticity of variance (CEV) model for an individual seeking to maximize the expected utility from cumulative consumption plus the expected utility from terminal wealth. Due to the fact that different individuals may have different risk preferences, we assume that the risk preference of an individual satisfies a hyperbolic absolute risk aversion (HARA) utility function. Generally speaking, power utility function, logarithmic utility function and exponential utility function widely used in investment theory are usually special cases of HARA utility function. By using the principle of dynamic programming and Legendre transform-dual technique, we obtain the explicit expression of the optimal investment-consumption decision. In addition, we derive the results under other utility functions as well and analyze some characteristics of the optimal portfolios and the optimal consumption decisions. A numerical simulation is presented to illustrate our results. Research results suggest that the optimal investment decisions between with consumption behavior and without it have considerable differences.

摘要

本文研究了在方差恒定弹性 (CEV) 模型下，个人寻求最大化累积消费的预期效用加上终端财富的预期效用的最优投资-消费决策。由于不同的个体可能有不同的风险偏好，我们假设个体的风险偏好满足双曲线绝对风险厌恶（HARA）效用函数。一般来说，投资理论中广泛使用的幂效用函数、对数效用函数和指数效用函数通常是HARA效用函数的特例。利用动态规划原理和勒让德变换对偶技术，得到了最优投资-消费决策的显式表达式。此外，我们也在其他效用函数下得出了结果，并分析了最优投资组合和最优消费决策的一些特征。给出了数值模拟来说明我们的结果。研究结果表明，有消费行为与无消费行为的最优投资决策存在较大差异。