Uncertain portfolio selection with mental accounts

Abstract

Since the security market is so complex, in real life, there are situations where the future security returns cannot be reflected by the past data and are given by experts' estimations according to their knowledge and judgement rather than by historical data. This paper discusses a portfolio selection problem in such an uncertain environment. In the paper, in order to reflect different attitudes towards risk that vary by goal in one portfolio investment, we apply mental account to the investment. Using uncertainty theory, we propose a new mean–variance uncertain portfolio selection model with mental accounts. Furthermore, we discuss the shape of the mean–standard deviation efficient frontier of the subportfolios of each mental account when security returns are normal uncertain variables and further give the condition where the optimal aggregate portfolio is on the mean–standard deviation efficient frontier. In addition, we compare the optimal portfolio with mental accounts with that without mental accounts. Finally, a numerical example is given as an illustration.