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

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.