Mean-risk model for uncertain portfolio selection with background risk

When making investment decisions, one will face not only the risk of financial assets within portfolio but also background risk. This paper discusses an uncertain portfolio selection problem in which background risk is considered and the security returns and background assets return are given by experienced experts' evaluations instead of historical data. Regarding the returns of the securities and background assets as uncertain variables, we propose an uncertain mean-risk model with background risk for portfolio selection and the crisp forms of the model are provided when security returns obey different uncertainty distributions. In addition, when everything else is same, it is concluded that the optimal expected return of the mean-risk model with background risk is usually smaller than that without background risk. Moreover, the relationship between the optimal solution of our model and that of the model in Huang's paper “Uncertain Portfolio Selection with Background Risk” is discussed. Finally, numerical examples are presented to illustrate the effectiveness of the model and to show the effect of background risk on investment decision.