There are many non-probabilistic factors that affect the financial markets such that the returns of risky assets may be regarded
as fuzzy numbers. This paper discusses the portfolio selection problem based on the possibilistic mean and variance of fuzzy
numbers, which can better described an uncertain environment with vagueness and ambiguity to compare with conventional probabilistic
mean-variance methodology. Markowitz’s mean-variance model is simplified a linear programming when returns of assets are symmetric
triangular fuzzy numbers, so the possibilistic efficient portfolios can be easily obtained by some related algorithms.
"Wang and Zhu , and Lai et al.  constructed interval programming models of portfolio selection. Zhang and Wang  and Zhang et al.  discussed the portfolio selection problem based on the (crisp) possibilistic mean and variance when short sales are not allowed at all risky assets. Watada , Ramaswamy , and Leon et al.  discussed portfolio selection using fuzzy decision theory. "
[Show abstract][Hide abstract] ABSTRACT: The objective of our research is to build a statistical test that can evaluate different risks of a portfolio selection model with fuzzy data. The central points and radiuses of fuzzy numbers are used to determine the portfolio selection model, and we statistically evaluate the best return by a fuzzy statistical test. Empirical studies are presented to illustrate the risk evaluation of the portfolio selection model with interval values. We conclude that the fuzzy statistical test enables us to evaluate a stable expected return and low risk investment with different choices for k, which indicates the risk level. The results of numerical examples show that our method is suitable for short-term investments.
IEICE Transactions on Information and Systems 03/2013; E96.D(3):579-588. DOI:10.1587/transinf.E96.D.579 · 0.21 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we define the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. We also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which are consistent with the extension principle. We also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.
Fuzzy Sets and Systems 09/2001; 122(2-122):315-326. DOI:10.1016/S0165-0114(00)00043-9 · 1.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Considering the uncertain returns of risky assets in capital markets as fuzzy numbers, we discuss the portfolio selection problem for bounded assets based on upper and lower possibilistic means and variances. The mean–standard deviation model for portfolio selection can be transformed to a linear programming under possibility distributions, so this methodology can be used to solve large-scale portfolio selection problems. A numerical example is used to illustrate our proposed effective means and approaches.
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