Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Abstract

Peng et al (Int J Uncertain Fuzziness Knowl Based Syst 15:29-41, 2007) introduced, by means of the credibility measure, two dominance relations on fuzzy variables, namely the first-and the second-order dominances. In this paper, we characterize each of these dominance relations, and we justify that they satisfy six well-known properties of comparison methods. We propose a Game Theory approach for the determination of optimal portfolios when returns are fuzzy by introducing the set of best portfolios with respect to the first-and the second-order dominances. Based on the characterization of the first-order dominance, we numerically display some of the best portfolios of the classical set of portfolios of seven independent assets described by triangular fuzzy numbers.

A Portfolio Choice Problem in the Framework of Expected Utility Operators

“…By particularization, we obtain the possibilistic expected utilities of [15], [16]. In addition, Tassak et al [29] and Sadefo et al [28] have developped an approach based on credibity theory which do not consider in this paper.…”