主管：中国科学院
主办：中国优选法统筹法与经济数学研究会
　　　中国科学院科技战略咨询研究院
Chinese Journal of Management Science

Chinese Journal of Management Science >

2016 , Vol. 24 >Issue 7: 11 - 17

DOI: https://doi.org/10.16381/j.cnki.issn1003-207x.2016.07.002

Articles

Multi-period Mean-semivariance Portfolio Selection with Minimum Transaction Lots Constraints

Expand
  • 1. School of Economics, Wuhan University of Technology, Wuhan 430070, China;
    2. School of Business Administration, South China University of Technology, Guangzhou 510641, China;
    3. School of Management, Wuhan University of Science and Technology, Wuhan 430081, China

Received date: 2013-12-29

  Revised date: 2015-01-04

  Online published: 2016-07-27

Fold

Abstract

In this paper the multi-period mean semivariance portfolio problem is dealt with minimum transaction lots considering, transaction costs, borrowing constraints and threshold constraints. In this case the problem of finding a feasible solution is NP-complete. An optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. The multi-period portfolio selection is the mix integer dynamic optimization problem with path dependence. The forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis with borrowing risk-free assets and without risk-free assets in the portfolio selection is provided by a numerical example to illustrate the efficiency of the proposed approaches and the designed algorithm.

Key words： multi-period portfolio selection; mean semivariance; minimum transaction lots; borrowing constraints; the forward dynamic programming method

Cite this article

ZHANG Peng, ZHANG Wei-Guo, ZHANG Yi-fei . Multi-period Mean-semivariance Portfolio Selection with Minimum Transaction Lots Constraints[J]. Chinese Journal of Management Science, 2016 , 24(7) : 11 -17 . DOI: 10.16381/j.cnki.issn1003-207x.2016.07.002

References

[1] Markowitz H. Portfolio selection[J]. Journal of Finance, 1952,7(1):77-91.

[2] Markowitz H. Portfolio selection:Efficient diversification of investments[M]. New York:Wiley, 1959.

[3] Deng Xiaotie, Li Zhongfei, Wang Shouyang. A minimax portfolio selection strategy with equilibrium[J]. European Journal of Operational Research, 2005, 166(1):278-292.

[4] Hirschberger M, Qi Yue, Steuer R E. Randomly generating portfolio-selection covariance matrices with specified distributional characteristics[J]. European Journal of Operational Research, 2007, 177(3):1610-1625.

[5] Grootveld H, Hallerbach W. Variance vs downside risk:Is there really that much difference?[J]. European Journal of Operational Research, 1999, 114(2):304-319.

[6] Fama E F. Portfolio analysis in a stable paretian market[J]. Management Science, 1965,11(3):404-419.

[7] Simkowitz M A, Beedles W L. Diversification in a three moment world[J]. Journal of Financial and Quantitative Annals, 1978,13(5):927-941.

[8] Leung M T, Daouk H, Chen Ansing. Using investment portfolio return to combine forecasts:A multiobjective approach[J]. European Journal Operations Research, 2001,134(1):84-102.

[9] Liu S C, Wang Shouyang, Qiu W H. Mean-variance-skewness model for portfolio selection with transaction costs[J]. International Journal Systems Science, 2003, 34(4):255-262.

[10] Unser M. Lower partial moments as measures of perceived risk:An experimental study[J]. Journal of Economic Psychology, 2000, 21(3):253-280.

[11] Rom B M, Ferguson K W. Post-modern portfolio theory comes of age[J]. Journal of Investing, 1994, 3(3):11-17.

[12] Roy A D. Safety first and the holding of assets[J]. Econometrica, 1952, 20(3):431-449.

[13] Huang Xiaoxia. Mean-semivariance models for fuzzy portfolio selection[J], Journal of Computational and Applied Mathematics, 2008, 217(1):1-8.

[14] Markowitz H,Todd P,Xu Ganlin,et al. Computation of mean-semivariance efficient sets by the critical line algorithm[J]. Annals of Operations Research, 1993, 45(1):307-317.

[15] Konno H, Wijayanayake A. Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints[J]. Mathematical Programming, 2001, 89(2):233-250.

[16] Speranza M G. A heuristic algorithm for a portfolio optimization model applied to the Milan Stock Market[J]. Computers and Operations Research, 1996, 23(5):433-441.

[17] Mansini R, Speranza M G. Heuristic algorithms for the portfolio selection problem with minimum transaction lots[J]. European Journal of Operational Research, 1999, 114(2):219-233.

[18] Kellerer H, Mansini R, Speranza M G. Selecting portfolios with fixed costs and minimum transaction lots[J]. Annals of Operations Research, 2000, 99(1):287-304.

[19] Lin Changchun, Liu Yiting. Genetic algorithms for portfolio selection problems with minimum transaction lots[J]. European Journal of Operational Research, 2008,185(1):393-404.

[20] Soleimani H, Golmakani H R, Salimi M H. Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm[J]. Expert Systems with Applications, 2009, 36(3):5058-5063.

[21] Golmakani H R, Fazel M. Constrained portfolio selection using particle swarm optimization[J]. Expert Systems with Applications, 2011, 38(7):8327-8335.

[22] Mossion J. Optimal multiperiod portfolio policies[J]. Journal of Business, 1968, 41(2):215-229.

[23] Hakansson N H. Multi-period mean-variance analysis:Toward a general theory of portfolio choice[J]. Journal of Finance, 1971, 26(4):857-884.

[24] Li Duan, Chan T F, Ng W L. Safety-first dynamic portfolio selection[J]. Dynamics of Continuous, Discrete and Impulsive, Systems Series B:Applications and Algorithms, 1998,4(4):585-600.

[25] Li Duan, Ng W L. Optimal dynamic portfolio selection:multiperiod mean-variance formulation[J]. Mathematical Finance, 2000,10(3):387-406.

[26] Calafiore G C. Multi-period portfolio optimization with linear control policies[J]. Automatica, 2008, 44(10):2463-2473.

[27] Zhu Shushang, Li Duan, Wang Shouyang. Risk control over bankruptcy in dynamic portfolio selection:a generalized mean-variance formulation[J]. IEEE Transactions on Automatic Control,2004,49(3):447-457.

[28] Gülp?nar N, Rustem B. Worst-case robust decisions for multi-period mean-variance portfolio optimization[J]. European Journal of Operational Research, 2007,183(3):981-1000.

[29] Yu Mei, Takahashi S, Inoue H, et al. Dynamic portfolio optimization with risk control for absolute deviation model[J]. European Journal of Operational Research, 2010, 201(2):349-364.

[30] Çlikyurt U, Öekici S. Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach[J]. European Journal of Operational Research, 2007, 179(1):186-202.

[31] Yan Wei, Li Shuyong. A class of multi-period semi-variance portfolio selection with a four-factor futures price model[J]. Journal of Applied Mathematics and Computing, 2009, 29(1):19-34.

[32] Yan Wei, Miao Rong, Li Shurong. Multi-period semi-variance portfolio selection:Model and numerical solution[J]. Applied Mathematics and Computation, 2007, 194(1):128-134.

[33] P?nar M Ç. Robust scenario optimization based on downside-risk measure for multi-period portfolio selection[J]. OR Spectrum, 2007, 29(2):295-309.

[34] Zhang Weiguo, Liu Yongjun, Xu Weijun. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs[J]. European Journal of Operational Research, 2012, 222(2):41-349.

[35] Zhang Weiguo, Liu Yongjun, Xu Weijun. A new fuzzy programming approach for multi-period portfolio Optimization with return demand and risk control[J]. Fuzzy Sets and Systems, 2014, 246(1):107-126.

[36] Liu Yongjun, Zhang Weiguo, Xu Weijun. Fuzzy multi-period portfolio selection optimization models using multiple criteria[J]. Automatica, 2012, 48(12):3042-3053.

[37] Liu Yongjun, Zhang Weiguo, Zhang Pu. A multi-period portfolio selection optimization model by using interval analysis[J]. Economic Modelling, 2013, 33:113-119.

[38] 袁子甲,李仲飞. 参数不确定性和效用最大化下的动态投资组合选择[J]. 中国管理科学,2010,18(5):1-6.

[39] 金秀,王佳,高莹. 基于动态损失厌恶投资组合模型的最优资产配置与实证研究[J].2014, 22(5):16-23.

[40] Deng Xue, Li Rongjun. A portfolio selection model with borrowing constraint based on possibility theory[J]. Applied Soft Computing, 2012, 12(2):754-758.

[41] Sadjadi S J, Seyedhosseini S M, Hassanlou Kh. Fuzzy multi period portfolio selection with different rates for borrowing and lending[J]. Applied Soft Computing, 2011, 11(4):3821-3826.

[42] Arnott R D, Wagner W H. The measurement and control of trading costs[J]. Financial Analysts Journal, 1990, 46(6):73-80.

[43] Yoshimoto A. The mean-variance approach to portfolio optimization subject to transaction costs[J]. Journal of the Operational Research Society of Japan, 1996, 39(1):99-117.

[44] Bertsimas D, Pachamanova D. Robust multiperiod portfolio management in the presence of transaction costs[J]. Computers and Operations Research, 2008, 35(1):3-17.

[45] Gulp?nar N, Rustem B, Settergren R. Multistage stochastic mean-variance portfolio analysis with transaction cost[J]. Innovations, in Financial and Economic Networks, 2003,(3):46-63.
Options
Outlines

/

〈 〉