Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory

Portfolio selection is one of the hottest issue in decision-making and management engineering. But due to the capital market natural complexity and investors’ irrational behaviors, it is not easy for investors to achieve their predefined goals. In this study, we propose a novel three-way decisions model based on cumulative prospect theory and outranking relations. Compared with traditional two-way decisions, the introduction of a boundary region into the three-way decisions theory makes it possible to reduce decision risk. By constructing an outranked set for each alternative and a hybrid multi-criteria decision-making matrix, three strategies are proposed by us to design the three-way decisions model. In order to test the effectiveness of the proposed model, we introduce it into a fuzzy multi-period portfolio selection case and design an improved particle swarm optimization as the solution algorithm. Finally, the effectiveness of the algorithm is validated by some test functions. And an experiment based on real market data validates the proposed multi-period portfolio selection model outperforms other compared models in terms of return, risk and risk-adjusted criteria.