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数学与物理
应用数学进展
Vol. 5 No. 1 (February 2016)
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不允许卖空证券组合投资模型的原始–对偶多项式内点算法
A Primal-Dual Polynomial Interior Point Method for Portfolio Investment without Short Sale
DOI:
10.12677/AAM.2016.51008
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作者:
田振明
,
宋馨雨
:广州中医药大学经济与管理学院,广东 广州
关键词:
证券组合
;
二次规划
;
内点算法
;
Portfolio
;
Quadratic Programming
;
Interior Point Method
摘要:
在分析Markowitz证券组合投资模型最优化解法的基础上,给出了求解不允许卖空证券组合投资模型的原始–对偶多项式内点算法;不同于传统牛顿法的迭代方向,借助一种新的工具寻找搜索方向,并且该算法具有多项式复杂性;用我们给出的算法对不允许卖空证券组合投资模型的实例进行计算求解,数值结果显示该算法是可行有效的。
Abstract:
Based on the optimal approach of Markowitz portfolio investment model, the algorithm of primal- dual polynomial interior point method to the above model was given. We applied this algorithm to solve an example of portfolio investment without short sale. Numerical implementation showed this method was practicable and effective.
文章引用:
田振明, 宋馨雨. 不允许卖空证券组合投资模型的原始–对偶多项式内点算法[J]. 应用数学进展, 2016, 5(1): 51-58.
http://dx.doi.org/10.12677/AAM.2016.51008
参考文献
[
1
]
Markowitz, H. (1952) Portfolio Selection. Journal of Finance, 7, 77-91.
http://dx.doi.org/10.1111/j.1540-6261.1952.tb01525.x
[
2
]
Markowitz, H. (1959) Portfolio Selection: Efficient Diversification of Investment. Besil Black-Well, Cambridge, 320- 335.
[
3
]
Ross, S.A. (1977) The Capital Asset Pricing Model, Short Sale Restriction and Related Issue. Journal of Finance, 32, 177-183.
http://dx.doi.org/10.1111/j.1540-6261.1977.tb03251.x
[
4
]
Voros, J. (1987) The Explicit Derivation of the Port-folio Frontier in the Case of Degeneracy and General Singularity. EJOR, 36, 302-311.
[
5
]
Dybvig, H. (1984) Short Sales Restriction and Kinds on the Mean-Variance Frontier. Journal of Finance, 39, 239-244.
http://dx.doi.org/10.1111/j.1540-6261.1984.tb03871.x
[
6
]
史树中, 杨杰. 证券组合选择的有效子集[J]. 应用数学学报, 2002, 25(1): 176-186.
[
7
]
史树中, 杨杰. 不允许卖空证券组合选择的有效子集[J]. 应用数学学报, 2003, 26(2): 286-299.
[
8
]
田振明. 奇异方差矩阵的Markowitz’s证券组合投资决策模型的最优化解法[J]. 数量经济技术经济研究, 2005, 22(10): 135-141.
[
9
]
田振明. 有效集法在确定Markowitz’s证券组合投资模型权系数中的应用[J]. 经济数学, 2007, 24(3): 239-243.
[
10
]
田振明. 不确定条件下具有容差项的Markowitz’s证券组合投资模型的最优化解法[J]. 数学理论与应用, 2013, 33(3): 48-56.
[
11
]
叶中行, 林建忠. 数理金融–资产定价与金融决策理论[M]. 北京: 科学出版社, 1998.
[
12
]
Antoniou, A. and Lu, W.-S. (2007) Practical Optimization: Algorithm and Engineering Applications. Springer, New York.
[
13
]
Kozlov, M.K. and Khachiyan, L.G. (1979) Polynomial Solvability of Convex Quadratic Programming. Soviet Mathematics Doklady, 20, 1108-1111.
[
14
]
Karmarkar, N.K. (1984) A New Polynomial-Time Algorithm for Linear Programming. Combinatorica, 4, 373-395.
http://dx.doi.org/10.1007/BF02579150
[
15
]
Ye, Y.Y. (1997) Interior-Point Algorithm Theory and Analysis. John Wiley and Sons, New York.
http://dx.doi.org/10.1002/9781118032701
[
16
]
Alizudeh, F. and Goldfarb, D. (2003) Second-Order Cone Pro-gramming. Mathematical Programming, 95, 3-15.
http://dx.doi.org/10.1007/s10107-002-0339-5
[
17
]
Bai, Y.Q., Eighamiand, M. and Roos, C. (2003) A New Effi-cient Large-Update Primal-Dual Interior-Point Method Based on a Finite Barrier. SIAM Journal on Optimization, 13, 766-782.
http://dx.doi.org/10.1137/S1052623401398132
[
18
]
Darvay (2002) A New Algorithm for Solving Self-Dual Linear Programming Problems. Studia Universitatis Babes- Bolyai, Seris Information, 47, 15-26.
[
19
]
Roos, C. (2006) A Full-Newton Step o(n) Infeasible Interior-Point Algorithm for Linear Optimization. SIAM Journal on Op-timization, 16, 1110-1136.
http://dx.doi.org/10.1137/050623917
[
20
]
Wright, S.J. (1997) Primal-Dual Inte-rior-Point Method. Society for Industrial and Applied Mathematics, Philadelphia.
http://dx.doi.org/10.1137/1.9781611971453
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