Abstract: Up to now, there is little research on the model with skewness and transaction cost based on the Markowitz mean-variance model, and there are less research results on this model integrated with Chinese market data and drawing three-dimensional efficiently portfolio frontier images. After setting up two kinds of optimal portfolio models under transaction cost constraints, regarding the linear combination of variance and skewness as objective function, two models are transformed approximately to problems of linear programming by the approximation of linear function. And the approximation degree can be controlled. Then simplex algorithm is applied to solve them to get the optimal portfolios. Depending on these, positive analysis is carried out to utilize the data of the eight Chinese listed companies and to draw approximate three-dimensional efficiently portfolio frontier images. Then the relationships between the objective optimization and parameters are discussed. It can be found that the objective function o is increasing function of expectation r and parameter m.

Key words: linear programming, portfolio model, skewness, transaction cost, efficient frontier images

摘要： 目前,在Markowitz的均值-方差模型基础上对含有偏度和交易成本模型的研究较少,结合国内市场数据进行研究并做出三维投资组合有效前沿图像的成果更少。在建立两种在交易成本约束条件下以方差和偏度的线性组合为目标函数的最优投资组合模型之后,利用线性函数逼近,将模型转换成线性规划问题,而且这种逼近程度可以控制。用单纯形法求解以得到最优投资组合。利用国内八个上市公司的数据进行实证分析,做出了三维投资组合近似有效前沿图像,并讨论了目标函数最优值和参数的关系。可以发现,目标函数是期望r和参数m的增函数。

关键词: 线性规划, 投资组合模型, 偏度, 交易成本, 有效前沿图像