奇异方差矩阵的Markowitz’s证券组合投资决策模型的最优化解法

An Optimal Approach to Markowitz's Portfolio Investment Model with Singular Covariance Matrices

基于Markowitz证券组合投资模型:min(1/2)W^tVW,s·t·W^te=1,W^tE(X)=μ_0,分析方差矩阵V为一般对称矩阵时的情形,本文推广了证券组合投资模型的一个定理,并分类讨论了一般对称方差矩阵对应的证券组合投资模型的最优解,同时给出了求解最优证券组合的方法。

In this paper, based on the model of Markowitz＇s Portfolio Invest 1 ment： min 1/2W^tVW, s.t.W^te=1, W^tE （X） =μ0, we study the model in which the covariance matrices are general symmetric matrices, get an extension on an important theorem, discuss the solution of the model following two classes of the gen eral symmetric matrices, and give a method for calculating optimal portfolio.