Portfolio selection based on upper and lower exponential possibility distributions

In this paper, two kinds of possibility distributions, namely, upper and lower possibility distributions are identi®ed to re ̄ect experts' knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution. In addition, a possibility risk can be de®ned as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to re ̄ect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches. Ó 1999 Elsevier Science B.V. All rights reserved.