奇异协方差阵下前沿组合及无套利分析  

Frontier Portfolio and No-arbitrage Analysis with Singular Covariance Matrix

作　　者：蒋春福[1] 戴永隆[1] 

机构地区：[1]中山大学数学与计算科学学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2005年第5期14-17,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10271120)

摘　　要：研究了奇异协方差阵的投资组合选择模型,运用镶边矩阵广义逆方法得到了存在前沿组合的充要条件,并给出了前沿组合的显式解和组合前沿的性质。最后,在奇异协方差阵下进行了无套利分析,得到了市场无套利的充要条件,证明了Szego的猜想。Portfolio choice model with singular covariance matrix is investigated. Not only the necessary and sufficient conditions for existing frontier portfolio in the capital market are obtained, but also the implicit general solutions of frontier portfolio and some properties of portfolio frontier are derived through the generalized inverse of bordered matrix. Finally, no-arbitrage analysis of the financial market with singular covariance matrix are made, and the necessary and sufiqcient condition for not existing abritarge portfolio is obtained, which proves the conjecture proposed by Szego.

关 键 词：奇异协方差阵 证券组合 组合前沿 无套利分析 

分 类 号：F830.9[经济管理—金融学] O212.1[理学—概率论与数理统计]