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Fuzzy mean-variance-skewness portfolio selection models by interval analysis. (English) Zbl 1207.91059
Summary: In the portfolio selection problem, the expected return, risk, liquidity etc. cannot be predicted precisely. The investor generally makes his portfolio decision according to his experience and his economic wisdom. So, deterministic portfolio selection is not a good choice for the investor. In most of the recent works on this problem, fuzzy set theory is widely used to model the problem in uncertain environments. This paper utilizes the concept of interval numbers in fuzzy set theory to extend the classical mean-variance (MV) portfolio selection model into mean-variance-skewness (MVS) model with consideration of transaction cost. In addition, some other criteria like short and long term returns, liquidity, dividends, number of assets in the portfolio and the maximum and minimum allowable capital invested in stocks of any selected company are considered. Three different models have been proposed by defining the future financial market optimistically, pessimistically and in the combined form to model the fuzzy MVS portfolio selection problem. In order to solve the models, fuzzy simulation (FS) and elitist genetic algorithm (EGA) are integrated to produce a more powerful and effective hybrid intelligence algorithm (HIA). Finally, our approaches are tested on a set of stock data from Bombay Stock Exchange (BSE).

91G10 Portfolio theory
26E50 Fuzzy real analysis
65G30 Interval and finite arithmetic
Full Text: DOI
[1] L. Bachelier, Theorie de la Speculation: Thesis: Annales Scientifiques de l’École Normale Superieure (1900); I I I 17; 21-86.
[2] Markowitz, H., Portfolio selection, Journal of finance, 7, 77-91, (1952)
[3] Samuelson, P., The fundamental approximation theorem of portfolio analysis in terms of means, variances an higher moments, Review of economic studies, 25, 65-86, (1958)
[4] Lai, T., Portfolio selection with skewness: a multiple – objective approach, Review of the quantitative finance and accounting, 1, 293-305, (1991)
[5] Konno, H.; Suzuki, K., A mean – variance – skewness optimization model, Journal of the operations research society of Japan, 38, 137-187, (1995) · Zbl 0839.90012
[6] Chunhachinda, P.; Dandapani, K.; Hamid, S.; Prakash, A.J., Portfolio selection and skewness: evidence from international stock markets, Journal of banking and finance, 21, 143-167, (1997)
[7] Liu, S.C.; Wang, S.Y.; Qiu, W.H., A mean – variance – skewness model for portfolio selection with transaction costs, International journal of system science, 34, 255-262, (2003) · Zbl 1074.91533
[8] Prakash, A.J.; Chang, C.; Pactwa, T.E., Selecting a portfolio with skewness: recent evidence from US, European and Latin American equity markets, Journal of banking and finance, 27, 1375-1390, (2003)
[9] Briec, W.; Kerstens, K.; Jokung, O., Mean – variance – skewness portfolio performance gauging: a general shortage function and dual approach, Management science, 53, 135-149, (2007) · Zbl 1232.91609
[10] Yu, L.; Wang, S.Y.; Lai, K., Neural network based mean – variance – skewness model for portfolio selection, Computers and operations research, 35, 34-46, (2008) · Zbl 1139.91347
[11] S. Ramaswamy, Portfolio selection using fuzzy decision theory, Working paper of Bank for International Settlements, 59, 1998.
[12] Parra, M.A.; Terol, A.B.; Uría, M.V.R., A fuzzy goal programming approach to portfolio selection, European journal of operational research, 133, 287-297, (2001) · Zbl 0992.90085
[13] Zhang, W.; Nie, Z., On admissible efficient portfolio selection problem, Applied mathematics and computation, 159, 357-371, (2004) · Zbl 1098.91065
[14] Bilbao-Terol, A.; Perez-Gladish, B.; Arenas-Parra, M.; Urfa, M.R., Fuzzy compromise programming for portfolio selection, Applied mathematics and computation, 173, 251-264, (2006) · Zbl 1138.91421
[15] Gupta, P.; Mehlawat, M.K.; Saxena, A., Asset portfolio optimization using fuzzy mathematical programming, Information sciences, 178, 1734-1755, (2008) · Zbl 1132.91464
[16] Huang, X., Mean – semivariance models for fuzzy portfolio selection, Journal of computational and applied mathematics, 217, 1-8, (2008) · Zbl 1149.91033
[17] Huang, X., Risk curve and fuzzy portfolio selection, Computers and mathematics with applications, 55, 1102-1112, (2008) · Zbl 1142.91527
[18] Lin, C.C.; Liu, Y.T., Genetic algorithms for portfolio selection problems with minimum transaction lots, European journal of operational research, 185, 393-404, (2008) · Zbl 1137.91461
[19] Bhattacharyya, R.; Kar, M.B.; Kar, S.; Dutta Majumder, D., (), 603-608
[20] Li, X.; Qin, Z.; Kar, S., Mean – variance – skewness model for portfolio selection with fuzzy returns, European journal of operational research, 202, 239-247, (2010) · Zbl 1175.90438
[21] Grattan-Guinness, I., Fuzzy membership mapped onto interval and many valued quantities, Mathematical logic quarterly, 22, 149-160, (1976) · Zbl 0334.02011
[22] Jahn, K.U., Interval-wertige mengen, Mathematische nachrichten, 68, 115-132, (1975) · Zbl 0317.02075
[23] R. Sambuc, Functions \(\Phi\)-floues, Applications á l’aide au diagonostic en pathologie thyroidienne, Ph.D. Thesis, University of Marseille, 1975.
[24] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning-I, Information sciences, 8, 199-249, (1975) · Zbl 0397.68071
[25] Cornelis, C.; Deschrijver, G.; Kerre, E.E., Advances and challenges in interval-valued fuzzy logic, Fuzzy sets and systems, 157, 622-627, (2006) · Zbl 1098.03034
[26] K.T. Atanassov, Intutionistic fuzzy sets. VII ITKR’s Session, Sofia (1983), decomposed in Central Sci.-Technical Library of Bulg. Acad. Of Sci. 1697/84 (in Bulgarian).
[27] Gau, W.L.; Buehrer, D.J., Vague sets, IEEE transactions on systems, man and cybernetics, 23, 2, 610-614, (1993) · Zbl 0782.04008
[28] Alefeld, G.; Mayer, G., On the symmetric and unsymmetric solution set of interval systems, SIAM journal on matrix analysis and applications, 16, 1223-1240, (1995) · Zbl 0834.65012
[29] Lai, K.K.; Wang, S.Y.; Xu, J.P.; Zhu, S.S.; Fang, Y., A class of linear interval programming problems and its application to portfolio selection, IEEE transactions on fuzzy systems, 10, 698-704, (2002)
[30] Ida, M., Portfolio selection problem with interval coefficients, Applied mathematics letters, 16, 709-713, (2003) · Zbl 1076.91016
[31] Ida, M., Solutions for the portfolio selection problem with interval and fuzzy coefficients, Reliable computing, 10, 389-400, (2004) · Zbl 1087.91026
[32] Giove, S.; Funari, S.; Nardelli, C., An interval portfolio selection problems based on regret function, European journal of operational research, 170, 253-264, (2006) · Zbl 1079.91030
[33] Fang, Y.; Lai, K.K.; Wang, S.Y., Portfolio rebalancing model with transaction costs based on fuzzy decision theory, European journal of operational research, 175, 879-893, (2006) · Zbl 1142.91521
[34] Ehrgott, M.; Klamroth, K.; Schwehm, C., An MCDM approach to portfolio optimization, European journal of operational research, 155, 752-770, (2004) · Zbl 1043.91016
[35] Hansen, E., Global optimization using interval analysis, (1992), Marcel Dekker New York · Zbl 0762.90069
[36] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
[37] Rommerlfanger, H.; Hanscheck, R.; Wolf, J., Linear programming with fuzzy objectives, Fuzzy sets and systems, 29, 31-48, (1989)
[38] Ishihuchi, H.; Tanaka, M., Multiobjective programming in optimization of the interval objective function, European journal of operational research, 48, 219-225, (1990) · Zbl 0718.90079
[39] Sakawa, M., Fuzzy sets and interactive multiobjective optimization, (1993), Plenum Press New York · Zbl 0842.90070
[40] Carlsson, C.; Fuller, R., On possibilistic Mean value and variance of fuzzy numbers, Fuzzy sets and systems, 122, 315-326, (2001), 2001 · Zbl 1016.94047
[41] Holland, J.H., Adaptation in natural and artificial systems, (1975), University of Michigan Press Ann Arbor
[42] Bhandari, D.; Murthy, C.A.; Pal, S.K., Genetic algorithm with elitist model and its convergence, International journal of pattern recognition and artificial intelligence, 10, 6, 731-747, (1996)
[43] Huang, X., Fuzzy chance-constrained portfolio selection, Applied mathematics and computation, 177, 500-507, (2006) · Zbl 1184.91191
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