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

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