×

Portfolio selection based on fuzzy probabilities and possibility distributions. (English) Zbl 1028.91551

Summary: Two kinds of portfolio selection models are proposed based on fuzzy probabilities and possibility distributions, respectively, rather than conventional probability distributions in Markowitz’s model. Since fuzzy probabilities and possibility distributions are obtained depending on possibility grades of security data offered by experts, investment experts’ knowledge can be reflected. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches.

MSC:

91G10 Portfolio theory
60A99 Foundations of probability theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Dubois, D.; Prade, H., Possibility theory, (1988), Plenum Press New York · Zbl 0645.68108
[2] Markowitz, H.M., Portfolio selection: efficient diversification of investments, (1959), Wiley New York
[3] Tanaka, H., Fuzzy data analysis by possibilistic linear models, Fuzzy sets and systems, 24, 363-375, (1987) · Zbl 0633.93060
[4] H. Tanaka, P. Guo, Portfolio selection method based on possibility distributions, Proc. 14th Internat. Conf. on Production Research, vol. 2, 1997, pp. 1538-1541.
[5] H. Tanaka, P. Guo, H.-J. Zimmermann, Possibility distributions of fuzzy variables in fuzzy linear programming problems, Proc. 7th Internat. Fuzzy Systems Association World Congress, vol. 3, 1997, pp. 48-52.
[6] H. Tanaka, P. Guo, Identification methods for exponential possibility distributions, Proc. 6th IEEE Internat. Conf. on Fuzzy Systems, vol. 2, 1997, pp. 687-692.
[7] Tanaka, H.; Hayashi, I.; Watada, J., Possibilistic linear regression analysis for fuzzy data, European J. oper. res., 40, 389-396, (1989) · Zbl 0669.62054
[8] Tanaka, H.; Ishibuchi, H., Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters, Fuzzy sets and systems, 41, 145-160, (1991) · Zbl 0734.62072
[9] Tanaka, H.; Ishibuchi, H., Evidence theory of exponential possibility distributions, Internat. J. approximate reasoning, 8, 123-140, (1993) · Zbl 0778.68083
[10] Tanaka, H.; Ishibuchi, H.; Yoshikawa, S., Exponential possibility regression analysis, Fuzzy sets and systems, 69, 305-318, (1995) · Zbl 0842.62062
[11] H. Tanaka, H. Nakayama, A. Yanagimoto, Possibility portfolio selection, Proc. 4th IEEE Internat. Conf. on Fuzzy Systems, 1995, pp. 813-818.
[12] Zadeh, L.A., Probability measures of fuzzy events, J. math. anal. appl., 22, 421-427, (1968) · Zbl 0174.49002
[13] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.