协方差矩阵奇异情况下的最优投资组合

基金项目:

国家自然科学基金(10171066)

上海市科委重点项目(02DJ14063).

详细信息

Optimal Mean-Variance Portfolio with Semi-Positive Variance-Covariance Matrix

Department of Mathematics, Institute for Contemporary Finance, Jiao tong University, Shanghai 200030

摘要: 本文讨论了在方差-协方差矩阵半正定条件下,Markowitz均值-方差最优投资组合模型的求解问题,利用主成分分析法得到了解析解,从而弥补了原模型的一个缺陷.
- Markowitz均值-方差模型 /
- 主成分分析 /
- 两基金定理
Abstract: An approach based on principal component analysis is proposed for solving the problem of optimal portfolio in the case with semi-positive variance-covariance matrix. Analytic solution is obtained. This result fills up the gap of the original Markowitz’s model.

[1]	Markowitz, H., Portfolio selection, Journal of Finance, 7(1)(1952), 77-91.
[2]	Markowitz, H., Portfolio Selection: Efficient Diversification of Investment, Wiley, New York, 1952.
[3]	Merton, R.C., An analytic derivation of the efficient portfolio frontier, Journal of Financial and Quantitative. Analysis, 7(1972), 1851-1872.
[4]	Fama, E., Foundation of Finance, Basic Books, Inc, Publishers, 1976.
[5]	Korn, R., Optimal Portfolio, World Scientific Publishing Co. Pte. Ltd, Singapore, 1997.
[6]	Buser, S.A., Mean-variance portfolio selection with either a singular or nonsingular variance- covariance matrix, Financial and Economic Research Section Division of Research, HB- 135-B88, 1976.
[7]	叶中行,林建忠,数理金融一资产定价与金融决策理论,北京,科学出版社, 1998.
[8]	Jurczenko, E. and Maillet, B., The three-moment CAPM: Theoretical Foundations and an Asset Pricing Model Comparison in a Unified Framework, Developments in Forecast Combination and Portfolio Choice, Eds by C. Dunis etc, John Wiley & Sons, 239-273, 2001.
[9]	程云鹏,矩阵论,西北工业大学出版社,1989.
[10]	北京大学数学系几何与代数教研室代数小组编,高等代数(第二版),高等教育出版社,2000.