Mean-Variance Adjusting Model for Portfolio Selection Problem with Fuzzy Random Returns

In this paper, we consider portfolio adjusting problem in the environment with multiple uncertainties. We establish two kinds of mean-variance adjusting models. The first one is formulated by only taking into account the transaction costs, and the second one is established by simultaneously considering transaction costs and minimum transaction lots. In the situation that all the returns are symmetrical triangular fuzzy random variables, these two models are converted into equivalent deterministic forms which are mixed-integer nonlinear programming models. Finally, a numerical example is given to illustrate the modelling idea.