不允许卖空下证券投资组合的区间二次规划问题

中国管理科学 ›› 2012, Vol. ›› Issue (3): 57-62.

不允许卖空下证券投资组合的区间二次规划问题

徐晓宁, 何枫

北京科技大学东凌经济管理学院, 北京 100083

收稿日期:2011-06-27 修回日期:2012-01-21 出版日期:2012-06-29 发布日期:2012-07-05
基金资助:
国家自然科学基金资助项目 (70802007,71172011);北京市2009年优秀人才计划项目(2009D 013001000012);中央高校基本科研业务费专项资金资助项目(FRF-TP-09-022A)

Interval Quadratic Programming for the Portfolio Selection without Short-Selling

XU Xiao-ning, HE Feng

Dongling School of Economics and Management, Beijing University of Science & Technology, Beijing 100083, China

Received:2011-06-27 Revised:2012-01-21 Online:2012-06-29 Published:2012-07-05

摘要/Abstract

摘要： 本文基于经典的Markowitz均值-方差模型,针对市场上不允许卖空的情况,提出了证券投资组合的区间二次规划模型,通过应用区间数排序方法(区间序关系、区间可能度和区间可接受度),给出了两种证券投资组合的区间非线性优化的数学转化模型,从而将不确定性证券投资组合模型转化为确定性的证券投资组合二次规划模型进行求解,并对由本文给出的三种求解方法与传统方法进行了比较。

关键词: 证券投资组合, 区间数, 区间二次规划, 满意解

Abstract: Based on the Markowitz M-V theory, interval quadratic programming model of portfolio investment is proposed in this paper. In the case of no short sales of assets, this model is solved by applying approaches to compare any two intervals and introducing acceptability and possibility degree of interval number. Thus uncertainty model of portfolio investment is coverted into certainty quadratic programming model of portfolio investment. In addition, for the solution of interval quadratic programming, three solutions of the model given in this paper are compared with the traditional one.

Key words: portfolio selection, interval number, interval quadratic programming, satisfactory solution

中图分类号:

O221

徐晓宁, 何枫. 不允许卖空下证券投资组合的区间二次规划问题 [J]. 中国管理科学, 2012, (3): 57-62.

XU Xiao-ning, HE Feng. Interval Quadratic Programming for the Portfolio Selection without Short-Selling[J]. Chinese Journal of Management Science, 2012, (3): 57-62.

参考文献

[1] Ida M.Portfolio selection problem with interval coefficients [J]. Applied Mathematics Letters, 2003, 16(5): 709-713.
[2] Giove S, Funari S, Nardelli C. An interval portfolio problem based on regret function [J]. European Journal of perational Research, 2006, 170: 253-264.
[3] 陈华友, 赵玉梅. 基于区间数的证券组合投资模型研究 [J]. 大学数学, 2007, 23(1): 21-25.
[4] 陈国华, 袁转军, 廖小莲. 基于β约束的区间证券投资组合模型 [J]. 经济数学, 2008, 25(3): 254-256.
[5] Li Jun, Xu Jiuping. A novel portfolio selection model in a hybrid uncertain environment [J]. Omega, 2009, 37(2): 439-449.
[6] Liu S T, Wang R T. A numerical solution method to interval quadratic programming [J]. Applied Mathematics and Computation, 2007, 189: 1274-1281.
[7] Li Wei, Tian Xiaoli. Numerical solution method for general interval quadratic programming[J]. Applied Mathematics and Computation, 2008, 202: 589-595.
[8] 徐泽水, 达庆利. 一种基于可能度的区间判断矩阵排序方法 [J]. 中国管理科学, 2003, 11(1): 63-65.
[9] 李炳军, 刘思峰. 一种基于区间数判断矩阵的群决策新方法 [J]. 中国管理科学, 2004, 12(6): 109-112.
[10] 马龙华. 不确定系统的鲁棒优化方法及其研究. 杭州: 浙江大学, 2002.
[11] 郭均鹏, 吴育华. 超效率DEA模型的区间扩展 [J]. 中国管理科学, 2005, 13(2): 40-43.
[12] 陆志鹏, 王洁方, 刘思峰, 方志耕. 区间DEA 模型求解算法及其在项目投资效率评价中的应用 [J]. 中国管理科学, 2009, 17(4): 165-169.
[13] Chanas S, Kuchta D. Multiobjective programming in optimization of interval objective functions-a generalized approach [J]. European Journal of Operational Research, 1996, 94: 594-598.
[14] 刘宝碇, 赵瑞清, 王纲. 不确定规划及应用 [M]. 北京: 清华大学出版社, 2003.
[15] 刘新旺, 达庆利. 一种区间数线性规划的满意解 [J]. 系统工程学报, 1999, 14(2): 123-128.
[16] Sengupta A, Pal T K, Chakraborty D. Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming[J]. Fuzzy Sets and Systems, 2001, 119: 129-138.
[17] 郭均鹏, 吴育华. 区间线性规划的标准型及其求解[J]. 系统工程, 2003, 21(3): 79-82.
[18] 孙海龙, 姚卫星. 区间数排序方法评述 [J]. 系统工程学报, 2010, 25(3): 304-312.