This paper considers the Merton portfolio optimization problem for an investor that aims at maximizing the expected power utility of the terminal wealth and intermediate consumption. Applying the homotopy analysis method, an analytical solution for value function as well as optimal strategy under the 3/2 model is derived, respectively. Compared with the existing explicit solutions for Merton problem under the 3/2 model, the formulas provide certain parameters with less requirement since the homotopy analysis method does not depend on the existence of small parameters in the equation. Finally, numerical examples are examined with the approach, and the proposed solution provides more accurate approximation as the number of terms in infinite series increases.

本文考虑了旨在使终端财富和中间消费的预期电力效用最大化的投资者的默顿投资组合优化问题。应用同伦分析法，分别推导了3/2模型下价值函数的解析解和最优策略。与现有的3/2模型下的Merton问题的显式解相比，由于同伦分析方法不依赖于方程中小参数的存在，因此这些公式提供的参数较少，因此要求较少。最后，使用该方法检查了数值示例，并且随着无限级数项的增加，所提出的解决方案提供了更准确的近似值。