Possibilistic mean-variance utility to portfolio selection for bounded assets

Abstract

Compared with the conventional probabilistic mean-variance methodology, fuzzy number can better describe an uncertain environment with vagueness and ambiguity. Based on this fact, possibilistic mean-variance utilities to portfolio selection for bounded assets are discussed in this paper. The possibilistic mean value of the expected return is termed measure of investment return and the possibilistic variance of the expected return is termed measure of investment risk. Moreover, we propose three kinds of optimization portfolio selection models under assumption each investor’s utility is the mean-variance type function: (I) a quadratic programming model for upper possibilistic mean-variance utility; (II) a quadratic programming model for lower possibilistic mean-variance utility; and (III) a quadratic programming model with a parameter for weighted upper and lower mean-variance utility. Finally, a numerical example of the portfolio selection problem is given to illustrate our proposed effective upper and lower possibilistic means, variances and approaches, which can be regarded as a natural extension of Carlsson et al.(2002) (possibilistic mean-variance utility to portfolio selection without bounded assets).