Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory

Abstract

This paper discusses an uncertain multi-period portfolio selection problem in the situation where the future security return rates are given by experts’ estimations instead of historical data. In financial market, investors may have different attitudes towards risk for different goals. In order to reflect these conflicting risk attitudes for different goals, mental accounts are introduced to the investment. In addition, investment strategies may be affected by some realistic constraints such as background risk, liquidity risk, transaction cost and cardinality constraint. Based on uncertainty theory, a nonlinear multi-period portfolio selection model is proposed with consideration of mental accounts and realistic constraints. In the model, indeterminate quantities such as security return rates and turnover rates are assumed to be uncertain variables. Within the framework of uncertainty theory, we discuss the equivalents of the model and show that the nonlinear model can be equivalently transformed into a linear programming model. Finally, a case study is given to illustrate the performance of the proposed model.