Portfolio selection models in uncertain environment

It is difficult that the security returns are reflected by previous data for portfolio selection (PS) problems. In order to overcome this, we take security returns as uncertain variables. In this paper, two portfolio selection models are presented in uncertain environment. In order to express divergence, the cross-entropy of uncertain variables is introduced into these mathematical models. In two models, we use expected value to express the investment return. At the same time, variance or semivariance expresses the risk, respectively. The mathematical models are solved by the gravitation search algorithm proposed by E. Rashedi. We apply the proposed models to two examples to exhibit effectiveness and correctness of the proposed models.