考虑投资组合收益率完全分布信息的投资组合优化研究

前四阶矩并不能完全决定收益率服从何种分布,因而对于偏好某种特定分布的投资者而言,以往的高阶投资组合优化方法并不适用,应当进行考虑投资组合收益率完全分布信息的投资组合优化。本文提出了一种考虑投资组合收益率完全分布信息的投资组合优化方法,通过Gram-Charlier渐进展开来近似投资组合收益率的概率密度函数,以KL散度来度量投资组合收益率的概率密度函数与目标概率密度函数的距离,从而构建了投资组合优化模型,并给出了具体算例。

Portfolio Optimization with Fully Distribution Information of Portfolio return

The first four moments couldn’ t determine totally the distribution of asset return,so the familiar portfolio optimization with higher moments isn’ t appropriate and the portfolio optimization with fully distribution information of portfolio return should be handled for investors preferable to the certain distribution.In this paper,the method of portfolio optimization with fully distribution information of portfolio return is put forward,where the density function of portfolio return is approximated to through Gram-Charlier expansions and the distance between density function of portfolio return and objective density function is measured through KL Divergence and the Numerical example is followed.