作　　者： ; ; ; ;

机构地区： 西安交通大学管理学院

出　　处： 《系统工程学报》 2005年第1期6-11,共6页

摘　　要： Markowitz基于概率理论建立了有名的均值方差证券组合模型,文章则基于模糊理论建立了一类具有权系数的均值方差证券组合模型.首先对证券市场上的收益与风险特性重新进行度量和刻画,提出了一类新的具有加权的可能性均值、方差及协方差的概念,类似于概率论中均值方差的分析讨论了这些概念的性质.其次基于该文定义的均值方差,建立了以收益率为模糊数的加权可能性证券组合投资模型,并给出了相应的加权可能性有效证券组合及有效前沿概念.通过求解两个相对应的优化模型得到了一个具有带状投资区域的有效前沿.尤其当资产收益率具有线性或分段线性隶属函数的模糊数时,该证券组合选择模型实质上为一个线性规划问题,因此有效前沿可化为一个具有折线段的带状投资区域. Markowitz proposes the famous mean-variance model based on probability theory, while a class of weight coefficient mean-variance model in this paper is developed based on fuzzy theory. Firstly, we reconsider the characteristics of return rate and risk in security market, and define the new notions of the weighted possibilistic mean values and variances and covariances. These notions' properties are discussed on a similar manner as mean and variance in probability theory. Secondly, the weighted possibilistic portfolio models are presented on them. We also introduce the conceptions of the weighted possibilistic efficient portfolios and efficient frontiers. Moreover, the efficient frontier like a band shape is given out by calculating two relatively optimal models. Especially, when return rates of assets are fuzzy numbers with linear or segmented linear membership functions, the portfolio model is in fact a linear programming problem. Then its efficient frontier is the investment region like a band shape with linear segments.

关 键 词： 模糊数 可能性原理 证券组合选择 有效证券组合 有效前沿

领　　域： [经济管理]