基于随机矩阵理论的Markowitz 组合投资模型

唐晓清1, 白延琴1, 刘念祖2, 刘莹3

doi:10.3969/j.issn.1007-2861.2013.03.014

上海大学学报(自然科学版) >

2013 , Vol. 19 >Issue 3: 293 - 297

DOI: https://doi.org/10.3969/j.issn.1007-2861.2013.03.014

数理化科学

基于随机矩阵理论的Markowitz 组合投资模型

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1. 上海大学理学院, 上海 200444; 2. 上海立信会计学院数学与信息学院, 上海 201620; 3. 邵阳学院理学系, 湖南邵阳 422000

收稿日期: 2012-09-21

网络出版日期: 2013-06-30

基金资助

国家自然科学基金资助项目(11071158)

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Markowitz Portfolio Model Based on Random Matrix Theory

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1. College of Sciences, Shanghai University, Shanghai 200444, China; 2. School of Mathematics and information, Shanghai Lixin University of Commerce, Shanghai 201620, China; 3. Science Department, Shaoyang University, Shaoyang 422000, Hunan, China

Received date: 2012-09-21

Online published: 2013-06-30

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摘要

通过随机矩阵方法识别、消除极端或非无关抽样样本, 提高Markowitz 模型的参数估计精度, 改进应用Markowitz 模型的效果;同时, 针对抽样不足的情况, 使用Bootstrap 方法较好地解决了该问题.

关键词： Bootstrap 方法; Markowitz 组合投资模型; 随机矩阵理论

本文引用格式

唐晓清1, 白延琴1, 刘念祖2, 刘莹3 . 基于随机矩阵理论的Markowitz 组合投资模型[J]. 上海大学学报(自然科学版), 2013 , 19(3) : 293 -297 . DOI: 10.3969/j.issn.1007-2861.2013.03.014

Abstract

Markowitz’s mean-variances model in this paper is improved, and the random matrix theory is used that can identify extreme sampling data and relevance data to get rid of those data such that more accurate estimate of mean and variance can be gotten. Then Bootstrap method to solve the problem of insufficient
sample is used.

Key words： andom matrix theory (RMT); Bootstrap method; Markowitz portfolio model;

参考文献

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[2] 唐晓清, 谭明纯. 简单序约束条件下参数估计的EM方法[J]. 湖南工程学院学报, 2010, 20(1): 61-64.

[3] 唐晓清, 王汉兴. 识别药物最小有效剂量的逐步方法[J]. 药物评价研究, 2010, 33(1): 58-62.

[4] Frankfurther G M, Phillips H E, Seagle J P. Portfolio selection: the effects of uncertain mean, variances, and covariance [J]. Journal of Financial and Quantitative Analysis, 1971(6): 1251-1262.

[5] Michaud R O. The Markowitz optimization enigma: is “optimized” optimizal? [J]. Financial Analysis, 1989, 45(1): 31-42.

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[8] Bai Z D, Liu H X, Wong W K. Enhancement of the applicability of Markowitz’s portfolio optimization by utilizing random matrix theory [J]. Mathematical Finance, 2009, 4(19): 639-667.

[9] 刘念祖, 王汉兴, 唐晓清, 等. 基于连续重新评估方法寻找药物的最大安全剂量[J]. 药物评价研究, 2011, 34(6): 425-427.

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