Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States

In previous studies, there were few portfolio models involving investors’ psychological states, market ambiguity and entropy. Some entropy can make the model have the effect of diversifying investment, which is very important. This paper mainly studies four kinds of entropy. First, we obtained four definitions of entropy from the literature, and gave the function of fuzzy entropy in different psychological states through strict mathematical proof. Then, we construct a fuzzy portfolio entropy decision model based on the investor’s psychological states, and compared it with the possibilistic mean–variance model. Then we presented a numerical example and compared the five different models established. By comparing the results, we find that: (a) The possibilistic mean–Shannon entropy model solves the problem of the possibility of excessive concentration in the possibilistic mean–variance model, but the dispersion is not enough. Conversely, the possibilistic mean–Yager entropy is over–emphasized due to the definition of its own function, such that it gave an investment pattern of equal weight distribution or approximate average distribution. (b) The results of possibilistic mean–proportional entropy can be said to be the middle status of the portfolios of possibilistic mean–Shannon entropy and possibilistic mean–Yager entropy. This portfolio not only achieves a certain rate of return, but also disperses the risk to some extent. (c) The lines of satisfaction for portfolios derived from different models are approximately U–shaped with the increase in return preference. (d) The possibilistic mean–Shannon entropy model tends to have the highest portfolio satisfaction with the same psychological state of the investor.