CREDIBILISTIC PARAMETER ESTIMATION AND ITS APPLICATION IN FUZZY PORTFOLIO SELECTION

Document Type: Research Paper

Authors

1 The State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

2 School of Economics and Management, Beihang University, Beijing 100191, China

3 Department of Mathematical Sciences, University of Cincinnati, Cincin- nati, Ohio 45221, USA

Abstract

In this paper, a maximum likelihood estimation and a minimum
entropy estimation for the expected value and variance of normal fuzzy variable
are discussed within the framework of credibility theory. As an application,
a credibilistic portfolio selection model is proposed, which is an improvement
over the traditional models as it only needs the predicted values on the security
returns instead of their membership functions.

Keywords


[1] A. R. Arabpour and M. Tata, Estimating the parameters of a fuzzy linear regression model,
Iranian Journal of Fuzzy Systems, 5(2) (2008), 1-20.
[2] K. Cai, Parameter estimations of normal fuzzy variables, Fuzzy Sets and Systems, 55 (1993),
179-185.
[3] H. Dishkant, About membership functions estimation, Fuzzy Sets and Systems, 5 (1981),
141-147.
[4] D. Dubois and H. Prade, Possibility theory: an approach to computerized processing of un-
certainty, Plenum, New York, 1998.
[5] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, A note on evaluation of fuzzy linear
regression models by comparing membership functions, Iranian Journal of Fuzzy Systems,
6(2) (2009), 1-6.
[6] X. Huang, Portfolio selection with fuzzy returns, Journal of Intelligent & Fuzzy Systems,
18(4) (2007), 383-390.
[7] M. Javadian, Y. Maali and N. Mahdavi-Amiri, Fuzzy linear programming with grades of
satisfaction in constraints, 6(3) (2009), 17-35.
[8] X. Li and B. Liu, A sucient and necessary condition for credibility measures, International
Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, 14(5) (2006), 527-535.
[9] X. Li and B. Liu, Maximum entropy principle for fuzzy variables, International Journal of
Uncertainty, Fuzziness & Knowledge-Based Systems, 15(Supp.2) (2007), 43-52.
[10] X. Li, Z. Qin and S. Kar, Mean-variance-skewness model for portfolio selection with fuzzy
parameter, European Journal of Operational Research, 202(1) (2010), 239-247.
[11] P. Li and B. Liu, Entropy of credibility distributions for fuzzy variables, IEEE Transactions
on Fuzzy Systems, 16(1) (2008), 123-129.
[12] B. Liu, Uncertainty theory, 2nd ed., Springer-Verlag, Berlin, 2007.
[13] B. Liu and Y. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE
Transactions on Fuzzy Systems, 10(4) (2002), 445-450.
[14] H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91.
[15] S. Nahmias, Fuzzy variables, Fuzzy Sets and Systems, 1 (1978), 97-110.
[16] Z. Qin, X. Li and X. Ji, Portfolio selection based on fuzzy cross-entropy, Journal of Compu-
tational and Applied Mathematics, 228(1) (2009), 139-149.
[17] D. Ralescu, Toward a general theory of fuzzy variables, Journal of Mathematical Analysis
and Applications, 86 (1982), 176-193.
[18] M. Sugeno, Theory of fuzzy integrals and its applications, PhD. Thesis, Tokyo Institute of
Technology, 1974.

[19] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1
(1978), 3-28.