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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/10/1125 |
| _version_ | 1797551839949881344 |
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| author | Xue Deng Tao Lin Chuangjie Chen |
| author_facet | Xue Deng Tao Lin Chuangjie Chen |
| author_sort | Xue Deng |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:50:46Z |
| format | Article |
| id | doaj.art-791b3a7412484f7b95ea51e9d7d6f065 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:50:46Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-791b3a7412484f7b95ea51e9d7d6f0652023-11-20T16:02:14ZengMDPI AGEntropy1099-43002020-10-012210112510.3390/e22101125Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological StatesXue Deng0Tao Lin1Chuangjie Chen2School of Mathematics, South China University of Technology, Guangzhou 510640, ChinaSchool of Mathematics, Sun Yat–Sen University, Guangzhou 510275, ChinaSchool of Mathematics, South China University of Technology, Guangzhou 510640, ChinaIn 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.https://www.mdpi.com/1099-4300/22/10/1125portfolio modeldifferent psychological statespossibility theoryvarious entropy measures |
| spellingShingle | Xue Deng Tao Lin Chuangjie Chen Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States Entropy portfolio model different psychological states possibility theory various entropy measures |
| title | Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States |
| title_full | Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States |
| title_fullStr | Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States |
| title_full_unstemmed | Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States |
| title_short | Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States |
| title_sort | comparison and research on diversified portfolios with several entropy measures based on different psychological states |
| topic | portfolio model different psychological states possibility theory various entropy measures |
| url | https://www.mdpi.com/1099-4300/22/10/1125 |
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