基于随机β系数的模糊随机投资规划——金融市场在其中所起的作用

The Fuzzy Random Investment Programming Based on the RandomβCoefficient

根据资本资产定价模型分析模式,将传统的β系数修订为度量证券市场随机不确定性的随机因子,将证券的β系数映射到模糊不确定环境中。在均值-半绝对偏差分析框架,构造出目标函数能同时反映证券市场随机不确定性和模糊不确定性的梯形模糊随机投资收益,风险约束为模糊容差松弛约束的模糊随机投资规划模型,并得到了有效性前沿。利用中国证券市场上的真实数据进行实证检验,得出如下结论:随机β系数有效描述了梯形模糊随机收益中所蕴含的随机性因素;规划具有一定程度的可靠性;投资规划体现出较好的持续性;投资规划在上涨行情中的投资效果要优于下跌行情中的投资效果,基于大流通市值的股票的模糊随机投资规划具有较好的持续性。

According to the model of capital asset pricing model,the traditionalβcoefficient was revised to the random factor which used for measuring the random uncertainty of the stock market,and theβcoefficient of the security was mapped to the fuzzy uncertainty environment.In the analytical framework of the mean-semi-absolute deviation,we construct the fuzzy random programming which the objective function is the trapezoidal fuzzy random investment return which can reflect both the random uncertainty and the fuzzy uncertainty of the security market and the risk constrains is the fuzzy tolerance relaxation constrain,then obtain the efficient frontier.Used the real data of the China security market to empirical analyze,it shows that the randomβcoefficient can describe the random factors in the trapezoidal fuzzy random investment return effectively;the programming is reliability in certain degree;the programming reflects a better continuity;the investment effect of the investment programming in the rising prices of the security market is better than the one in the decline prices of the security market,and the fuzzy random investment programming based on the large market capitalization stocks has better continuity.