Research and comparison of uncertain portfolio selection model with background risk and mental accounts

Considering the uncertainty of financial market and the investor's different attitudes towards risk caused by the various goals, in this paper, a portfolio selection problem with background risks and mental accounts constraints is studied to explore their impact on investment decisions. Firstly, we establish a model with normal uncertain variables, and the optimal solutions of portfolio models with and without background risk are compared. Secondly, considering that the investors always divide an account into several sub-accounts, we put forward an uncertain portfolio model combining uncertainty theory and mental account theory. Thirdly, a portfolio model with background risk and mental accounts is proposed, and the total expected returns of the models in with different proportions of mental accounts are compared. Finally, some numerical applications are provided to validate the model. The result shows that when the levels of tolerance are the same, the expected return of a portfolio with background risk is lower than that without background risk. In addition, the result also shows that when the percent of savings account decreases and that of the consumption account increases, the total expected return increases.