Investment decision making based on the probabilistic hesitant financial data: model and empirical study

This paper proposes a portfolio selection model from the perspective of probabilistic hesitant financial data (PHFD). PHFD can be interpreted as the new form of information presentation that is obtained by transforming real financial data into probabilistic hesitant fuzzy elements. Based on the above data and model, we can derive the optimal investment ratios and give suggestions for investors. Specifically, this paper first develops a transformation algorithm to transform the general share returns into PHFD. The transformed data can directly show all the returns and their occurrence probabilities. Then, the portfolio selection and risk portfolio selection models based on PHFD, namely the probabilistic hesitant portfolio selection (PHPS) model and the risk probabilistic hesitant portfolio selection (RPHPS) model, are proposed. Furthermore, the investment decision-making methods are provided to show their practical application in financial markets. It is pointed out that the PHPS model for general investors is constructed based on the maximum-score or minimum-deviation principles to get the optimal investment ratios, and the RPHPS model provides the optimal investment ratios for three types of risk investors with the aim of obtaining the maximum return or taking the minimum risk. Finally, an empirical study based on the real data of China’s stock markets is shown in detail. The results verify the effectiveness and practicability of the proposed methods.