Fuzzy portfolio optimization for time-inconsistent investors: a multi-objective dynamic approach

In recent years, fuzzy optimization has been widely adopted to handle the nonstatistical uncertainties in portfolio selection. Meanwhile, various risk measurements, including variance, entropy and value at risk, have been introduced in fuzzy environments to evaluate portfolio risks from different perspectives. In this study, we discuss fuzzy multi-objective dynamic portfolio optimization for time-inconsistent investors. When building the model, variance and value at risk as the representatives of different types of risk measurements are employed together with the expected return. And a dynamic investment policy is developed for time-inconsistent investors, which combines the expected return and value at risk into one objective. Then, the model is established to maximize the cumulative combined objective function and minimize the cumulative portfolio variance simultaneously. In addition, a multi-objective dynamic evolutionary algorithm is designed as a possible solution of the proposed model. The effectiveness of this research is demonstrated by using a real market data-based case study. Experimental results demonstrate that the proposed model matches the practical behavior of time-inconsistent investors and the solution algorithm is feasible to solve the complicated nonlinear problem.