证券组合的模糊优化

Fuzzy Optimization of Securities Combination

在双目标有价证券选择基础上 ,将模糊概念运用于有价证券组合选择 ,按投资者给定的期望目标及容差 ,以隶属度为目标函数 ,讨论了线性隶属函数与非线性隶属函数模型·当隶属函数在 [0 ,1]之间取值时 ,两模型的解无大的差异 ,并反映出投资者的满意程度·与线性隶属函数相比 ,非线性隶属函数的参数对应收益率及风险的模糊尺度 ,其取值越大 ,模糊尺度越小 ,能更好地反映出投资者对目标值的取值意图·依据深圳股票市场 10只股票收益率数据 ,采用进化规划进行优化计算 ,并验证模型的有效性·

On the basis of two securities selection, the fuzzy concept was applied to the portfolio composition selection. According to the hope, object and permitting difference given by investor, the membership was taken as object function. The models of the linear membership function and the non linear membership function were discussed. When the membership function takes value between [0,1], the solution of two models has no big difference and reflects,the satisfatory degree of the customer. The parameter of the non linear membership function corresponds to the fuzzy scale of the investor's profit rate and the risk. These values are smaller and the fuzzy scale is smaller compared with the linear membership function. It is well shown that the investor takes the value intention for the object value .For the data of ten stock profit rate in Shen Zhen stock market, the evolution programming is adopted to wage the optimization calculation and to verify the effectiveness of the model.