Abstract
This paper is concerned with a fuzzy version of the portfolio selection problem, which includes diversification conditions and incorporates investor’s subjective preferences. The inclusion of diversification conditions leads to mixed-integer models, which are computationally demanding. On the other hand, the consideration of integer conditions makes the solution very sensitive to investor’s subjective preferences with regard to the trade-off between risk and expected return. These preferences are imprecise by their very nature. In this paper, we overcome these issues by proposing a solution method for a fuzzy quadratic portfolio selection model with integer conditions. The suitability of the proposed method is illustrated by means of two numerical examples.
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References
Markowitz, H.M.: Portfolio selection. J. Financ. 7, 77–91 (1952)
Markowitz, H.M.: Portfolio Selection: Efficient Diversification of Investments. Wiley, New York (1959)
Inuiguchi, M., Ramík, J.: Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets Syst. 111, 3–28 (2000)
Tanaka, H., Guo, P., Türksen, I.B.: Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets Syst. 3, 387–397 (2000)
Watada, J.: Fuzzy portfolio selection and its applications to decision making. Tatra Mt. Math. Publ. 13, 219–248 (1997)
Gupta, P., Inuiguchi, M., Mehlawat, M.K., Mittal, G.: Multi-objective credibilistic portfolio selection model with fuzzy chance-constraints. Inform. Sci. 229, 1–17 (2013)
Cadenas, J.M., Carrillo, J.V., Garrido, M.C., Ivorra, C., Liern, V.: Exact and heuristic procedures for solving the fuzzy portfolio selection problem. Fuzzy Opt. Decis. Mak. 11, 29–46 (2012)
Jana, P., Roy, T.K., Mazumder, S.K.: Multi-objective possibilistic model for portfolio selection with transaction cost. J. Comput. Appl. Math. 228, 188–196 (2009)
Jiménez, M., Bilbao, A.: Pareto-optimal solutions in fuzzy multi-objective linear programming. Fuzzy Sets Syst. 160, 2714–2721 (2009)
Calvo, C., Ivorra, C., Liern, V.: The geometry of the efficient Frontier of the portfolio selection problem. J. Financ. Decis. Mak. 7, 27–36 (2011)
Calvo, C., Ivorra, C., Liern, V.: On the computation of the efficient frontier of the portfolio selection problem. J. Appl. Math. (2012). doi:10.1155/2012/105616
Fama, E.F.: Foundations of Finance. Basic Books, New York (1976)
Huang, C.-F., Litzenberg, R.H.: Foundations for Financial Economics. North Holland, Amsterdam (1988)
León, T., Liern, V., Vercher, E.: Viability of infeasible portfolio selection problems: a fuzzy approach. Eur. J. Oper. Res. 139, 178–189 (2002)
León, T., Liern, V., Vercher, E.: Fuzzy mathematical programming for portfolio management. In: Bonilla, M., Casasús, T., Sala, R. (eds.) Financial Modelling. Physica-Verlag, Heidelberg (2000)
Zimmermann, H.J.: Fuzzy mathematical programming. In: Gal, T., Greenberg, H.J. (eds.) Advances in Sensitivity Analysis and Parametric Programming. Kluwer, Dordrecht (1997)
Delgado, M., Verdegay, J.L., Vila, M.A.: Fuzzy linear programming: from classical methods to new applications. In: Delgado, M., Kacprzyk, J., Verdegay, J.L., Vila, M.A. (eds.) Fuzzy Optimization: Recent Advances. Physica Verlag, Heidelberg (1988)
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Communicated by Moawia Alghalith.
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Calvo, C., Ivorra, C. & Liern, V. Fuzzy Portfolio Selection Including Cardinality Constraints and Integer Conditions. J Optim Theory Appl 170, 343–355 (2016). https://doi.org/10.1007/s10957-016-0902-5
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DOI: https://doi.org/10.1007/s10957-016-0902-5