| 摘要: |
| 基于全球经济动态的复杂性，人们往往不能准确识别风险因素演化的规律，金融建模本质上不可避免受制于模型的模糊性。针对投资者对平均收益率和波动率的估计存在疑虑而产生风险模糊厌恶心理问题，提出一个带有常数绝对风险厌恶效用函数的封闭式投资组合优化方法；给定一个实现紧凑值的波动率，使用特殊不确定性集表示漂移，利用最优化问题的Karush-Kuhn-Tucher条件，基于经典默顿问题以及极大-极小、哈密顿-雅可比-贝尔曼-艾萨克（Hamilton-Jacobi-Bellman-Isaacs）偏微分方程可求出模糊厌恶投资者在市场上的最优投资组合。 |
| 关键词: 默顿问题 CARA效用 波动率不确定性 Hamilton-Jacobi-Bellman-Isaacs 方程 |
| DOI： |
| 分类号: |
| 基金项目: |
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| The General Merton Problem of an Ambiguity Averse Investor |
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CHEN Lin, CHEN Xiao-yan
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| Abstract: |
| Based on the complexity of global economic dynamics, people often cannot accurately identify the evolution of risk factors. Inevitably, financial modeling is inherently subject to the ambiguity of the model. The Ayersberg paradox believes that people repulse the ambiguity, that is, people are more inclined to choose certain things, and to reject things which are uncertain. A closed loop portfolio optimization method with a constant absolute risk aversion utility function is proposed to solve the problem of risk ambiguity and aversion of investors' doubts about the average yield and volatility. Given a volatility that achieves compact values, using a special uncertainties set to represent drift, using the Karush-Kuhn-Tucher condition of the optimization problem, based on the classical Dyson problem and the max-minimum Hamilton-Jacobi-Berman-Isaacs partial differential equation, the optimal portfolio for ambiguity aversive investors can be solved. |
| Key words: Merton problem CARA utility volatility uncertainty Hamilton-Jacobi-Bellman-Isaacs equation |
