基于熵的投资组合优化模型的研究综述

A Review of the Optimal Portfolio Model Based on Entropy

Markowitz定义的以证券收益率的方差为证券风险的度量方式存在计算复杂、高估风险(高于期望收益的部分也视为风险的范畴)和收益率分布只能是正态分布的局限性.为了解决这种风险度量的局限性,研究了证券投资组合理论的风险度量方法,本着尽可能分散投资风险的原则,从信息熵的定义出发,构建了基于随机不确定熵、模糊不确定熵、模糊随机不确定熵的三种投资组合模型,提出的模型满足各种不同投资环境中对应的模型,使对证券投资组合模型的应用和研究更客观合理.

Markowitz gives the definition of measuring the risk of security by using the variance of the return rate,but the definition has the following three limitations：the computation is too complex,the risk is higher（the part which is higher than the expected return is also taken as the risk of the security）and the distribution of the returns is just in a normal distribution.In order to solve the limitation of this risk measurement,this paper studies the risk measurement by using information entropy.According to the principle of diversifying investment risk as much as possible,three different models are constructed：stochastic uncertainty entropy model,fuzzy uncertainty entropy model and fuzzy stochastic uncertainty entropy model.Those proposed models can meet the needs of different constraints in various investment environments,and make the application and research of portfolio model more objective and reasonable.