A Multi-Objective Approach to Portfolio Optimization Problem Using the Analytic Hierarchy Process (AHP) and Genetic Algorithm

Document Type : Original Article

Authors

1 industrial engineering/ Bu ali Sina university/ Hamedan- Iran

2 Associate Professor, Department of Industrial Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran

Abstract

This study analyzes the portfolio optimization model, by considering the financial management and investment science in order to evaluate risks and return in regard with restrictions such as buyers’ assets for purchasing per share. Accordingly, a novel model is designed as linear programming in order to optimize the investment portfolio, considering the expected rate of return, the minimum risk, and the buyer’s assets. After the introduction of the model as linear programming and expressing the related limitations, different types of investments which an investor can consider in order to form an investment portfolio were studied. Finally, an approach is proposed to solve the model by using the genetic algorithm, and is implemented and analyzed in regard with a real example. According to the results of this study, the new model reduced downside risk in comparison with previously proposed models, in a manner that its stair descent continues as the number of shares under study increases.

Keywords

References

[1] HosseinDastkhan, Naser Shams Gharneh, HamidRezaGolmakani. _ A linguistic-based portfolio selection model using weighted max–min operator and hybrid genetic algorithm (2011).
[2] Chang-Chun Lin, Yi-Ting Liu_Genetic algorithms for portfolio selection problemswith minimum transaction lots (2008).
[3] Irina Bolshakova, Mikhail Kovalev_portfolio optimization problems (2009).
[4] Yousef Kilani_ Comparing the performance of the genetic and local search algorithms for solvingthesatisfiability problems (2010).
[5] Maciej Nowak_ Project Portfolio Selection Using Interactive Approach (2013).
[6] Lilian Noronha Nassif, João Carlos Santiago Filho, José Marcos Nogueira_ Project Portfolio Selection in Public Administration Using Fuzzy Logic (2013).
[7] Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7, 77–91.
[8] Markowitz, H. (1956). The optimization of a quadratic function subject to linear
constraints. Naval Research Logistics Quarterly, 3, 111–133.
[9] Markowitz, H, Todd, P, Xu, G, & Yamane, Y. (1993). Computation of mean-semi
variance efficient sets by the critical line algorithm. Annals of Operations Research, 45, 307–317.
[10] Speranza, M. Grazia. (1995). A Heuristics Algorithm for A Portfolio OptimizationModel Applied To the Milan Stock Market, Computer & Ops Res, 5,. 433-441.
[11] Fernandez, A. , Gomez, S. , "Portfolio Selection Using Neural Networks", Computers & Operations Research, No. 34, pp. 1177-1191, 2007.
[12] Tanaka, H. , Guo, P. , Turksen, I. B. , "Portfolio Selection Based on Fuzzy Probabilities and Possibility Distributions", Fuzzy sets and Systems, No. 111, pp. 387-397, 2000.
[13] Werner, J. C. , Fogarti, T. C. , "Genetic Control Applied to Asset Managements", EuroGP, LNCS, pp. 192-201,2002.
[14] Vafaei Jahan, M. , AkbarzadehTootonchi, M. R. , "Spin Glass Portfolio Selection," Proceeding of First Joint Congress on Fuzzy and Intelligent Systems, pp. 29-31, Aug 2007.
[15] Lin, C. M. , Gen, M. , "An Effective Decision-based Genetic Algorithm Approach to Multi-objective Portfolio Optimization Problem" , Applied Mathematical Sciences ,Vol. 1, No. 5, pp. 201-210, 2007.
[16] Anagnostopoulos, K. & Mamanis, G. (2009). Multiobjective evolutionary algorithms for complex portfolio optimization problems. Springer-Verlag, 8(3): 259-279.
[17] Derakhshan, M., Golmakani, H. & Hanafizadeh, P. (2012). Multiobjective Portfolio Selection of Tehran Stock Exchange with the Metaheuristic Optimization Approach. International Journal of Indestrial Engineering and Production Management, 23(3): 318-331. (in Persian).
[18] Khaleiji, M., Zeiaee, M., Tabei, A., Jahed-Motlagh, M.R. & Khaloozadeh, H. (2009). Dynamically Weighted Continuous Ant Colony Optimization for Bi- Objective Portfolio Selection Using Value-at-Risk. Third Asian International Conference on Digital Object Identifier, 1(2): 230-235.
[19] Mishra, S.K., Panda, G. & Meher, S. (2009). Multi-objective particle swarm optimization approach to portfolio optimization. World Congress on Nature & Biologically Inspired Computing. DOI:10.1109/NABIC.2009. 5393659.
[20] Skolpadungket, P., Dahal, K. & Harnpornchai, N. (2007). Portfolio optimization using multi-objective genetic algorithms. IEEE congress on evolutionary computation, CEC: 516-523. DOI: 10.1109/CEC.2007.4424514.
[21] Khaleiji, M., Zeiaee, M., Tabei, A., Jahed-Motlagh, M.R. & Khaloozadeh, H. (2009). Dynamically Weighted Continuous Ant Colony Optimization for Bi- Objective Portfolio Selection Using Value-at-Risk. Third Asian International Conference on Digital Object Identifier, 1(2): 230-235.
[22] Armananzas, R. & Lozano, J. A. (2005). A multiobjective approach to the portfolio optimization problem. IEEE congress on evolutionary computation, 2: 1388- 1395.
[23] Anagnostopoulos, K. & Mamanis, G. (2009). Multiobjective evolutionary algorithms for complex portfolio optimization problems. Springer-Verlag, 8(3): 259-279.
[24] Li, H. & Zhang, Q. (2009). Multiobjective Optimization Problems with Complicated Pareto Sets, MOEA/D and NSGA-II. IEEE Transactions on Evolutionary Comutation, 13(2): 284-302.
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