Uncertain portfolio selection with mental accounts and realistic constraints

Since the security market is too complex, there are situations where the future security returns cannot be reflected by historical data and have to be given by experts' estimations according to their knowledge and judgements. 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 accounts to the investment. Uncertain variables are introduced to describe the securities' return, and a new uncertain portfolio selection model is developed when return risk control and liquidity risk control are considered. In addition, other important limitations, i.e., transaction cost, minimum transaction lot, bounds of holding, security diversification and sector diversification are also considered. In real life, investors face background risk which may affect their portfolio selection decisions. Thus, background risk is also considered. To solve the proposed problem, the equivalents of the model are proposed. Finally, a numerical example is given as an illustration.