求解一类投资组合模型的混合算法  

A Hybrid Algorithm for Solving a Class of Markowitz Portfolio Models

作　　者：郭文秀 张崇涛 GUO Wen-xiu;ZHANG Chong-tao(School of Mathematics and Statistics,Shaoguan University,Shaoguan 512005,Guangdong,China)

机构地区：[1]韶关学院数学与统计学院,广东韶关512005

出　　处：《韶关学院学报》2022年第3期30-34,共5页Journal of Shaoguan University

基　　金：广东省大学生创新创业训练计划项目(S202110576048)。

摘　　要：Markowitz投资组合模型在实际中有广泛的应用,可通过模系变换转化为绝对值方程,对绝对值方程的解的分量符号进行分析,得到了相应的线性系统.进一步运用K-means聚类以及矩阵分裂迭代构建了混合算法.数值试验结果表明,本文构建的算法具有较高的计算效率,聚类技巧可以有效地发挥作用,对于一类Markowitz投资组合模型的求解,本文算法比Gauss-Seidel迭代收敛更快.Markowitz portfolio model is widely used in application and can be transformed to an absolute value equation by modulus transformation. In this paper, by the analysis of the signs of the solution’s items of absolute value equation, a corresponding linear system is obtained. Furthermore, a hybrid algorithm is proposed by K-means cluster technique and matrix splitting iteration. Numerical results show that the proposed algorithm can attain higher computational efficiency and the cluster technique works. Compared to Gauss-Seidel iteration, the proposed algorithm converges faster for solving a class of Markowitz portfolio models.

关 键 词：MARKOWITZ投资组合模型 线性系统 矩阵分裂 K-MEANS聚类 

分 类 号：O241.6[理学—计算数学]