Fuzzy portfolio selection based on three-way decision and cumulative prospect theory

The goal of fuzzy portfolio selection is to make a combination of securities which can maximize the return or minimize the risk. Most of existing studies assumed that the investor has all the cash in hand and no securities position before portfolio optimization, which is sometimes inconsistent to reality. Besides, many studies are based on expected utility theory, which is in conflict with the behavior of some investors and may also lead to over-concentration of capital. Therefore, in this paper, we propose a fuzzy portfolio selection model based on three-way decision and cumulative prospect theory, which can mitigate the two shortcomings mentioned above. In this model, every action in the action set to the candidate securities is assigned to a prospect value and we can construct a tri-partition of the candidate securities according to three-way decision theory. To validate the effectiveness of our approach, we adopted two case studies on the basis of real market data. The experimented results prove that the using of three-way decision and cumulative prospect theory increases the investment return, meanwhile, reduces the risk for the investor.