Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections
Empirical evidence suggests that financial risk has a heavy-tailed profile. Motivated by recent advances in the generalized quantile risk measure, we propose the tail value-at-risk (TVaR)-based expectile, which can capture the tail risk compared with the classic expectile. In addition to showing tha...
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/91 |
| _version_ | 1797431394316582912 |
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| author | Haoyu Chen Kun Fan |
| author_facet | Haoyu Chen Kun Fan |
| author_sort | Haoyu Chen |
| collection | DOAJ |
| description | Empirical evidence suggests that financial risk has a heavy-tailed profile. Motivated by recent advances in the generalized quantile risk measure, we propose the tail value-at-risk (TVaR)-based expectile, which can capture the tail risk compared with the classic expectile. In addition to showing that the risk measure is well-defined, the properties of TVaR-based expectiles as risk measures were also studied. In particular, we give the equivalent characterization of the coherency. For extreme risks, usually modeled by a regularly varying survival function, the asymptotic expansion of a TVaR-based expectile (with respect to quantiles) was studied. In addition, motivated by recent advances in distributionally robust optimization in portfolio selections, we give the closed-form of the worst-case TVaR-based expectile based on moment information. Based on this closed form of the worst-case TVaR-based expectile, the distributionally robust portfolio selection problem is reduced to a convex quadratic program. Numerical results are also presented to illustrate the performance of the new risk measure compared with classic risk measures, such as tail value-at-risk-based expectiles. |
| first_indexed | 2024-03-09T09:44:18Z |
| format | Article |
| id | doaj.art-02d10d16d9494909af79f54b66dac3bd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:44:18Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-02d10d16d9494909af79f54b66dac3bd2023-12-02T00:38:35ZengMDPI AGMathematics2227-73902022-12-011119110.3390/math11010091Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio SelectionsHaoyu Chen0Kun Fan1School of Data Science, University of Science and Technology of China, Hefei 230000, ChinaKey Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, 3663 North Zhongshan Road, Shanghai 200062, ChinaEmpirical evidence suggests that financial risk has a heavy-tailed profile. Motivated by recent advances in the generalized quantile risk measure, we propose the tail value-at-risk (TVaR)-based expectile, which can capture the tail risk compared with the classic expectile. In addition to showing that the risk measure is well-defined, the properties of TVaR-based expectiles as risk measures were also studied. In particular, we give the equivalent characterization of the coherency. For extreme risks, usually modeled by a regularly varying survival function, the asymptotic expansion of a TVaR-based expectile (with respect to quantiles) was studied. In addition, motivated by recent advances in distributionally robust optimization in portfolio selections, we give the closed-form of the worst-case TVaR-based expectile based on moment information. Based on this closed form of the worst-case TVaR-based expectile, the distributionally robust portfolio selection problem is reduced to a convex quadratic program. Numerical results are also presented to illustrate the performance of the new risk measure compared with classic risk measures, such as tail value-at-risk-based expectiles.https://www.mdpi.com/2227-7390/11/1/91expectilecoherent risk measureworst-case risk measuredistributionally robust optimizationheavy-tailed risks |
| spellingShingle | Haoyu Chen Kun Fan Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections Mathematics expectile coherent risk measure worst-case risk measure distributionally robust optimization heavy-tailed risks |
| title | Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections |
| title_full | Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections |
| title_fullStr | Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections |
| title_full_unstemmed | Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections |
| title_short | Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections |
| title_sort | tail value at risk based expectiles for extreme risks and their application in distributionally robust portfolio selections |
| topic | expectile coherent risk measure worst-case risk measure distributionally robust optimization heavy-tailed risks |
| url | https://www.mdpi.com/2227-7390/11/1/91 |
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