Portfolio selection and risk investment under the hesitant fuzzy environment.

The optimal investment ratios for a set of stocks and other financial products can be obtained by the conventional portfolio theory based on quantitative data such as returns and risks. However, quantitative data are sometimes unavailable, thus qualitative information provided by experts or decision makers should be used. Based on the foregoing, we propose new portfolio selection approaches based on such qualitative information which is represented herein as hesitant fuzzy elements. For general investors and risk investors, we develop two qualitative portfolio models based on the max-score rule and the score-deviation trade-off rule, respectively. Furthermore, the deviation and score trisection approaches are developed to distinguish the three types of risk investors, which also help to construct the corresponding qualitative portfolio models. In addition, we investigate the investment opportunities and efficient frontiers of these proposed qualitative portfolio models. Also, the specific portfolio selection processes are provided. Finally, an example of selecting the optimal portfolio of risk investment is provided. On the basis of the above study and example, we can conclude that the proposed qualitative portfolio models used for the three types of risk investors are effective. The given portfolio selection processes can be reasonably used in practical qualitative risk investment. [ABSTRACT FROM AUTHOR]