Using Fuzzy Possibilistic Mean and Variance in Portfolio Selection Model

A fuzzy portfolio selection method based on possibilistic mean and variance

“…Therefore, the membership function in this paper is a natural extension of Tanaka et al (2000), Guo et al (2002), Tanaka and Guo (1999), Zhang and Wang (2005), Zhang (2007), Carlsson et al (2002). The membership function f j (u), u ∈ R, whose value is interpreted as the degree of possibility of the statement that "r j (u) will be the rate of return on the ith asset" The detailed statements can be found in Inuiguchi and Tanino (2000), Tanaka et al (2000), Guo et al (2002), Tanaka and Guo (1999), Zhang and Wang (2005), Zhang (2007), Zhang et al (2007), Carlsson et al (2002).…”

“…Carlsson et al (2002) and Zhang (2007) introduced possibilistic approaches to select portfolios under the assumption that the returns of assets are trapezoidal fuzzy numbers. Zhang and Wang (2005) discussed the portfolio selection problem when returns of assets are symmetric triangular fuzzy numbers. Vasant (2006), Bhattacharya and Vasant (2007) researched fuzzy decision making problems using S-curve membership functions.…”

“…Carlsson et al (2002) introduced a possibilistic approach to selecting portfolios with highest utility score under the assumption that the returns of assets are trapezoidal fuzzy numbers. Zhang and Wang (2005), Zhang (2007) and Zhang et al (2007) discussed the portfolio selection problem based on the lower, upper and crisp possibilistic means and possibilistic variances introduced by Carisson and Fullër (2001), Zhang and Nie (2003). In this paper, we obtain a new possibilistic means-variance model for portfolio selection to replace Markowitz's mean-variance model when the returns of assets are L R-type fuzzy numbers.…”

“…They also showed that this expectation remains additive in the sense of addition of fuzzy numbers. Treating each return rate as a fuzzy number restricted by a possibility distribution, various possibilistic portfolio selection problems are discussed by Inuiguchi and Tanino (2000), Tanaka et al (2000), Guo et al (2002), Tanaka and Guo (1999), Carisson and Fullër (2001), Zhang and Nie (2003), Zhang and Wang (2005), Zhang (2007), Zhang et al (2007), Carlsson et al (2002), Vasant (2006), Bhattacharya and Vasant (2007), Inuiguchi et al (1992Inuiguchi et al ( , 1993. Tanaka and Guo (1999) proposed two kinds of portfolio selection models based on upper and lower exponential possibility distributions.…”

Risk Assessment of a Portfolio Selection Model Based on a Fuzzy Statistical Test

“…Wang and Zhu [30], and Lai et al [9] constructed interval programming models of portfolio selection. Zhang and Wang [39] and Zhang et al [38] discussed the portfolio selection problem based on the (crisp) possibilistic mean and variance when short sales are not allowed at all risky assets. Watada [28], Ramaswamy [22], and Leon et al [10] discussed portfolio selection using fuzzy decision theory.…”