The principal pivoting of pivoting algorithm for Markowitz's portfolio selection model is only needed under certain conditions and if a principal pivoting increases an asset into the portfolio, then the risk decreases, otherwise the risk increases.
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张忠桢. 马科维兹资产组合选择模型旋转算法的特点[J]. 科学技术与工程, 2002, (5): 62-64. ZHANG Zhongzhen. Characteristics of the Pivoting Algorithm for Markowitz Portfolio Selection Model[J]. Science Technology and Engineering,2002,(5):62-64.