奇异协方差阵及不同借贷利率下均值—方差模型的解析解

doi:10.12005/orms.2015.0064

运筹与管理 ›› 2015, Vol. 24 ›› Issue (2): 192-200.DOI: 10.12005/orms.2015.0064

奇异协方差阵及不同借贷利率下均值—方差模型的解析解

蒋春福¹, 彭泓毅²

1.深圳大学数学与计算科学学院,广东深圳 518060;
2.华南农业大学理学院,广东广州 510642

收稿日期:2011-05-21 出版日期:2015-04-12
作者简介:蒋春福(1977-),男,湖南永州人,博士,副教授,研究方向:投资组合,金融风险管理。
基金资助:
国家自然科学基金资助项目(71101095);广东省自然科学基金资助项目(2008276)

Analytic Solutions of Mean-Variance Model with Singular Covariance Matrix and Different Interest Rates for Borrowing and Lending

JIANG Chun-fu¹, PENG Hong-yi²

1.College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, China;
2.College of Science, South China Agricultural University, Guangzhou 510642, China

Received:2011-05-21 Online:2015-04-12

摘要/Abstract

摘要： 随着金融资产种类的增加,特别是考虑大规模投资组合问题时,很可能出现资产间的多重共线性或相关性,从而出现协方差阵奇异的情况。然而,目前关于投资组合的均值—方差分析大都是在协方差阵正定的条件下得到的,因此,不适用于奇异协方差阵的情形。针对这一问题,利用广义逆矩阵研究了协方差阵奇异时的均值—方差投资组合模型,在不同借贷利率条件下得到了前沿组合和组合前沿的解析解,突破了传统方法中要求协方差阵可逆的限制,推广了经典Markowitz模型。

关键词: 金融工程, 证券组合, Moore-Penrose广义逆, 不同借贷利率

Abstract: In the mean-variance portfolio model, the covariance matrix is likely to be singular since the multi-collinearity and correlation can arise from the increase of financial assets, especially when considering a large-scale portfolio. In view of this situation, we reconsider the mean-variance portfolio problem under singular covariance matrix. A new approach based on generalized inverse matrix is proposed as a remedy for the deficiency of conventional methods in which covariance matrix is constrained to be invertible. The analytic solutions of frontier portfolio and portfolio frontier are derived with different interest rates for borrowing and lending, which extending successfully the classic Markowitz portfolio model.

Key words: financial engineering, portfolio, moore-penrose generalized inverse, different interest rates for borrowing and lending

中图分类号:

F224
O212

蒋春福, 彭泓毅. 奇异协方差阵及不同借贷利率下均值—方差模型的解析解[J]. 运筹与管理, 2015, 24(2): 192-200.

JIANG Chun-fu, PENG Hong-yi. Analytic Solutions of Mean-Variance Model with Singular Covariance Matrix and Different Interest Rates for Borrowing and Lending[J]. Operations Research and Management Science, 2015, 24(2): 192-200.

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奇异协方差阵及不同借贷利率下均值—方差模型的解析解

Analytic Solutions of Mean-Variance Model with Singular Covariance Matrix and Different Interest Rates for Borrowing and Lending

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