A Fuzzy Mixed Integer Multi-Scenario Portfolio Optimization Model
In this paper, we propose a multiple objective optimization model with respect to portfolio selection problem for investors looking forward to diversify their equity investments in a number of equity markets. Based on Markowitz-s M-V model we developed a Fuzzy Mixed Integer Multi-Objective Nonlinear Programming Problem (FMIMONLP) to maximize the investors- future gains on equity markets, reach the optimal proportion of the budget to be invested in different equities. A numerical example with a comprehensive analysis on artificial data from several equity markets is presented in order to illustrate the proposed model and its solution method. The model performed well compared with the deterministic version of the model.
[1] Markowitz H. (1952) Portfolio Selection. Journal of Finance, 7: 77-91.
[2] Zhou H T, Wang Z J, Song H G. A multi-objective portfolio selection
model based on fuzzy optimization, Journal of Huazhong University of
Science and Technology (Natural Science), 2005, 33(1): 108-110.
[3] Zhuang X T, Huang X Y, Lu X. (2001), Fuzzy optimization of securities
combination, Journal of Northeastern University ( Natural Science),
22(2): 165-168.
[4] Zhang W. G. Possibilistic mean-standard deviation models to portfolio
for bounded assets, Applied Mathematics and Computation, 2007, 189:
1614-1623.
[5] Lacagnina V, Pecorella A. A stochastic soft constraints fuzzy model for
a portfolio selection problem, Fuzzy Sets and Systems, 2006, 157: 1317-
1327.
[6] Fang, F.H., Y., K., Liu, (2008), Mean Variance Models for portfolio
selection with Fuzzy Random Returns, Journal of Applied Mathematics
and Computations, DOI 10. 2007/s12190-008-0154-0.
[7] G. Zhang, Jie Lu, and F. Wu (2007), "On a generalized fuzzy goal
optimization for solving fuzzy multi-objective linear programming
problems", Journal of Intelligent & Fuzzy Systems 18, 83-97 IOS Press.
[8] Chen G., Chen S., Fang Y., Wang S,Y., Model for portfolio selection
with fuzzy return rates, Systems Engineering | Theory & Practice, July,
(2009), Vol.29, No.7, 1000-6788(2009)07-0008-08.
[9] Chen, G., Chen S., Fang Y., Wang S,Y., (2006) "A Possibilistic Mean-
VaR Model for Portfolio Selection Advanced Modeling and
Optimization", Vol. 8, No.1.
[10] Jun L., Jiuping, X. , A class of Possibilistic Portfolio Selection Model
with Interval Coefficients and its Application, Fuzzy Optimization and
Decision Making, Vol. 6, No. 2, June 2007 , pp. 123-137(15).
[11] SUPIAN S., (2007), On the Possibilistic Approach to a Portfolio
Selection Problem, Math. Reports 9(59), 3, 305-317.
[12] Guo, P and Tanaka, H., (2003), 'Portfolio selection with exponential
possibility distributions, "Fuzzy Portfolio Optimization", Lecture notes
in economics and mathematical systems LNEMS 609, Springer, 10, 117-
129.
[13] Ana F. Carazo. Trinidad Gomez, Julian Molina, Alfredo G. Hernandez-
Dial, Flor M. Guerrero, Rafael Caballero, (2010), "Solving a
comprehensive model for multi-objective project portfolio selection",
Computer and Operations Research, Vol. 37, Issue num 4 , pp 630-639.
[14] Takashi H., and Ishii H., (2007) ÔÇÿportfolio selection problem considering
fuzzy returns of future scenarios-, IEEE, 0-7695-2882-1/07.
[15] Takashi H., and Ishii H., (2008) 'Portfolio Selection Problems
Considering Fuzzy Returns Of Future Scenarios, International Journal of
Innovative Computing, Information and Control, Vol. 4, No. 10.
[1] Markowitz H. (1952) Portfolio Selection. Journal of Finance, 7: 77-91.
[2] Zhou H T, Wang Z J, Song H G. A multi-objective portfolio selection
model based on fuzzy optimization, Journal of Huazhong University of
Science and Technology (Natural Science), 2005, 33(1): 108-110.
[3] Zhuang X T, Huang X Y, Lu X. (2001), Fuzzy optimization of securities
combination, Journal of Northeastern University ( Natural Science),
22(2): 165-168.
[4] Zhang W. G. Possibilistic mean-standard deviation models to portfolio
for bounded assets, Applied Mathematics and Computation, 2007, 189:
1614-1623.
[5] Lacagnina V, Pecorella A. A stochastic soft constraints fuzzy model for
a portfolio selection problem, Fuzzy Sets and Systems, 2006, 157: 1317-
1327.
[6] Fang, F.H., Y., K., Liu, (2008), Mean Variance Models for portfolio
selection with Fuzzy Random Returns, Journal of Applied Mathematics
and Computations, DOI 10. 2007/s12190-008-0154-0.
[7] G. Zhang, Jie Lu, and F. Wu (2007), "On a generalized fuzzy goal
optimization for solving fuzzy multi-objective linear programming
problems", Journal of Intelligent & Fuzzy Systems 18, 83-97 IOS Press.
[8] Chen G., Chen S., Fang Y., Wang S,Y., Model for portfolio selection
with fuzzy return rates, Systems Engineering | Theory & Practice, July,
(2009), Vol.29, No.7, 1000-6788(2009)07-0008-08.
[9] Chen, G., Chen S., Fang Y., Wang S,Y., (2006) "A Possibilistic Mean-
VaR Model for Portfolio Selection Advanced Modeling and
Optimization", Vol. 8, No.1.
[10] Jun L., Jiuping, X. , A class of Possibilistic Portfolio Selection Model
with Interval Coefficients and its Application, Fuzzy Optimization and
Decision Making, Vol. 6, No. 2, June 2007 , pp. 123-137(15).
[11] SUPIAN S., (2007), On the Possibilistic Approach to a Portfolio
Selection Problem, Math. Reports 9(59), 3, 305-317.
[12] Guo, P and Tanaka, H., (2003), 'Portfolio selection with exponential
possibility distributions, "Fuzzy Portfolio Optimization", Lecture notes
in economics and mathematical systems LNEMS 609, Springer, 10, 117-
129.
[13] Ana F. Carazo. Trinidad Gomez, Julian Molina, Alfredo G. Hernandez-
Dial, Flor M. Guerrero, Rafael Caballero, (2010), "Solving a
comprehensive model for multi-objective project portfolio selection",
Computer and Operations Research, Vol. 37, Issue num 4 , pp 630-639.
[14] Takashi H., and Ishii H., (2007) ÔÇÿportfolio selection problem considering
fuzzy returns of future scenarios-, IEEE, 0-7695-2882-1/07.
[15] Takashi H., and Ishii H., (2008) 'Portfolio Selection Problems
Considering Fuzzy Returns Of Future Scenarios, International Journal of
Innovative Computing, Information and Control, Vol. 4, No. 10.
@article{"International Journal of Information, Control and Computer Sciences:50592", author = "M. S. Osman and A. A. Tharwat and I. A. El-Khodary and A. G. Chalabi", title = "A Fuzzy Mixed Integer Multi-Scenario Portfolio Optimization Model", abstract = "In this paper, we propose a multiple objective optimization model with respect to portfolio selection problem for investors looking forward to diversify their equity investments in a number of equity markets. Based on Markowitz-s M-V model we developed a Fuzzy Mixed Integer Multi-Objective Nonlinear Programming Problem (FMIMONLP) to maximize the investors- future gains on equity markets, reach the optimal proportion of the budget to be invested in different equities. A numerical example with a comprehensive analysis on artificial data from several equity markets is presented in order to illustrate the proposed model and its solution method. The model performed well compared with the deterministic version of the model.
", keywords = "Equity Markets, Future Scenarios, PortfolioSelection, Multiple Criteria Fuzzy Optimization", volume = "5", number = "11", pages = "1195-8", }
