Abstract
In this paper, a crisp possibilistic variance and a crisp possibilistic covariance of fuzzy numbers are defined, which is different from the ones introduced by Carlsson and Fullér. The possibilistic portfolio selection model is presented on the basis of the possibilistic mean and variance under the assumption that the returns of assets are fuzzy numbers. Especially, Markowitz’s probabilistic mean-variance model is replaced a linear programming model when the returns of assets are symmetric fuzzy numbers. The possibilistic efficient frontier can be derived explicitly when short sales are not allowed on all risky assets and a risk-free asset.
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References
Markowitz, H.: Portfolio selection: efficient diversification of Investments. Wiley, New York (1959)
Perold, A.F.: Large-scale portfolio optimization. Management Science 30, 1143–1160 (1984)
Pang, J.S.: A new efficient algorithm for a class of portfolio selection problems. Operational Research 28, 754–767 (1980)
Vörös, J.: Portfolio analysis-An analytic derivation of the efficient portfolio frontier. European journal of operational research 203, 294–300 (1986)
Best, M.J., Hlouskova, J.: The efficient frontier for bounded assets. Math. Meth. Oper. Res. 52, 195–212 (2000)
Watada, J.: Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematical Publication 13, 219–248 (1997)
Tanaka, H., Guo, P.: Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research 114, 115–126 (1999)
Tanaka, H., Guo, P., Burhan Türksen, I.: Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy sets and systems 111, 387–397 (2000)
Zadeh, L.A.: Fuzzy Sets. Inform. and Control 8, 338–353 (1965)
Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315–326 (2001)
Wang, S.Y., Zhu, S.S.: On fuzzy portfolio selection problems. Fuzzy Optimization and Decision Making 1, 361–377 (2002)
Zhang, W.G., Nie, Z.K.: On admissible efficient portfolio selection problem. Applied Mathematics and Compution 159, 357–371 (2004)
Zhang, W.G., Wang, Y.L.: Portfolio selection: Possibilistic mean-variance model and possibilistic efficient frontier. In: Megiddo, N., Xu, Y., Zhu, B. (eds.) AAIM 2005. LNCS, vol. 3521, pp. 203–213. Springer, Heidelberg (2005)
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Zhang, WG., Liu, WA., Wang, YL. (2005). A Class of Possibilistic Portfolio Selection Models and Algorithms. In: Deng, X., Ye, Y. (eds) Internet and Network Economics. WINE 2005. Lecture Notes in Computer Science, vol 3828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11600930_46
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DOI: https://doi.org/10.1007/11600930_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30900-0
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