收稿日期: 2014-12-05
修回日期: 2015-08-31
网络出版日期: 2016-01-15
基金资助
国家自然科学基金(11371340)资助
CVaR portfolio model based on K-means clustering with the constraint of generalized entropy
Received date: 2014-12-05
Revised date: 2015-08-31
Online published: 2016-01-15
构造带有广义熵约束的CVaR投资组合线性规划模型,采用K-means聚类法产生投资组合中各个资产收益率的情景及概率,并把它们代入模型中,得出投资组合的最优投资权数.通过选取深市的8只股票作为投资组合进行实证分析,并与MV模型对比,发现本模型不仅更能体现分散化投资的原则,且收益表现更好,具有较强的实用性.
关键词： K-means聚类算法; 广义熵; CVaR模型; 投资组合
吴文娣 , 程希骏 , 刘峰 . 基于K-means聚类和广义熵约束的CVaR投资组合模型[J]. 中国科学院大学学报, 2016 , 33(1) : 31 -36 . DOI: 10.7523/j.issn.2095-6134.2016.01.005
The present work constructs the CVaR linear programming model of portfolio with the constraint of generalized entropy. We generate scenarios and probabilities of each asset yield in the portfolio using the K-means clustering method. Then we substitute them into the model. Finally we get the optimal investment weights for various assets. The feasibility of this model is certificated by testing a portfolio which contains eight selected stocks in Shenzhen stock market. Compared with MV model, this model not only incorporates more decentralized investment principle, but also has better performance in the future yields. This model has strong practicability.
Key words： K-means clustering method; generalized entropy; CVaR model; portfolio
[1] Rockafellar R T, Uryasev S. Optimization of conditional value-at-risk[J]. Journal of Risk, 2000, 2(3): 21-41.
[2] Elahi Y, Abd Aziz M l. Mean-variance-CVaR model of multiportfolio optimization via linear weighted sum method[J]. Mathematical Problem in Engineering, 2014: 1-7.
[3] Meng Z Q, Jiang M, Hu Q Y. Dynamic CVaR with multi-period risk problems[J]. Journal of System & Complexity, 2011, 24(5): 907-918.
[4] 周世昊,倪衍森. 求解CVaR投资组合优化问题之改进PSO算法[J].武汉理工大学学报,2010,32(1):180-182.
[5] 张茂军,南江霞,高爱华.求解带有交易费用的CVaR投资组合模型的L-S算法[J].经济数学,2012,29(2):74-78.
[6] Rockafellar R T, Uryasev S. Conditional value-at-risk for general loss distributions[J].Journal of Banking and Finance, 2002, 26(7): 1 443-1 471.
[7] Krokhmal P, Palmquist J, Uryasev S. Portfolio optimization with condional value-at-risk objective and constraints[J]. The Journal of Risk, 2002, 4(2):124-129.
[8] 刘俊山.基于风险测度理论的证券投资组合优化研究 [D].上海:复旦大学,2007.
[9] 魏法明.基于随机规划动态投资组合中的情景元素生成研究 [D]. 上海:同济大学,2008.
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