不确定终止时间和通货膨胀影响下风险资产的最优投资策略

Optimal investment strategy for risky assets under uncertain time-horizon and inflation

本文基于连续时间均值-方差框架,研究了通货膨胀影响下投资终止时间不确定的最优投资组合选择问题.与以往大多数文献不同,本文所考虑的金融市场仅存在风险资产.首先构建了含通货膨胀及终止时间不确定因素的风险资产均值-方差投资组合选择模型.然后利用随机动态规划方法和Lagrange对偶原理得到了有效投资策略及有效边界的解析表达式,并进一步讨论了本文模型的几种特殊情形.最后,通过数值算例对本文所得结论进行阐述.

Based on a continuous-time mean-variance model, this paper considers a portfolio selection problem under inflation when time-horizon is uncertain. Different from most of the existing literature, the financial market considered in this paper consists of only risky assets. First of all, incorporating the uncertain factors of inflation and uncertain time-horizon, a mean-variance portfolio selection model with only risky assets is constructed. Second, closed-form expressions for efficient investment strategy and efficient frontier are derived by employing stochastic dynamic programming and Lagrange dual principle. Third, some special cases are discussed. Finally, a numerical example is provided to illustrate the results obtained in this paper.