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Mean-risk model for uncertain portfolio selection with background risk and realistic constraints

This paper studies a portfolio selection problem in such a situation where the future asset return rates cannot be well obtained by historical data but have to be given by experts' evaluations. In order to reflect the impact of realistic conditions on investment decisions, background risk and some realistic constraints are also considered. First, a nonlinear uncertain mean-risk model for uncertain portfolio selection is proposed. For further discussion, the crisp equivalent forms of the model are presented. Then, an effective solution method for solving the model is obtained. Furthermore, the influence of background risk on investment strategies is discussed by comparing the optimal expected return with background risk with that without background risk. Finally, some numerical examples are provided to illustrate the performance and applications of the model.