Conditional Tail Expectation and Premium Calculation under Asymmetric Loss
In this paper, we calculate premiums that are based on the Conditional Tail Expectation (CTE) and asymmetric loss functions to account for the risk of both underestimation and overestimation losses. After selecting an appropriate loss function, the premium is calculated as the quantity minimizing an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/5/496 |
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| author | Enrique Calderín-Ojeda Emilio Gómez-Déniz Francisco J. Vázquez-Polo |
| author_facet | Enrique Calderín-Ojeda Emilio Gómez-Déniz Francisco J. Vázquez-Polo |
| author_sort | Enrique Calderín-Ojeda |
| collection | DOAJ |
| description | In this paper, we calculate premiums that are based on the Conditional Tail Expectation (CTE) and asymmetric loss functions to account for the risk of both underestimation and overestimation losses. After selecting an appropriate loss function, the premium is calculated as the quantity minimizing an objective function related to the conditional tail expectation of the loss. The premium satisfies desirable properties, i.e., it is a coherent risk measure, and it helps the practitioner to quantify the global risk of the insurer. Finally, this methodology is applied to quantify the risks associated to the total claims amount that are modelled via composite models and comparisons with the usual risk measures, i.e., Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are carried out. |
| first_indexed | 2024-03-11T03:56:56Z |
| format | Article |
| id | doaj.art-a9fda92b43094f108cfb442b798ee989 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T03:56:56Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-a9fda92b43094f108cfb442b798ee9892023-11-18T00:28:06ZengMDPI AGAxioms2075-16802023-05-0112549610.3390/axioms12050496Conditional Tail Expectation and Premium Calculation under Asymmetric LossEnrique Calderín-Ojeda0Emilio Gómez-Déniz1Francisco J. Vázquez-Polo2Centre for Actuarial Studies, University of Melbourne, Melbourne, VIC 3010, AustraliaDepartment of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, SpainDepartment of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, SpainIn this paper, we calculate premiums that are based on the Conditional Tail Expectation (CTE) and asymmetric loss functions to account for the risk of both underestimation and overestimation losses. After selecting an appropriate loss function, the premium is calculated as the quantity minimizing an objective function related to the conditional tail expectation of the loss. The premium satisfies desirable properties, i.e., it is a coherent risk measure, and it helps the practitioner to quantify the global risk of the insurer. Finally, this methodology is applied to quantify the risks associated to the total claims amount that are modelled via composite models and comparisons with the usual risk measures, i.e., Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are carried out.https://www.mdpi.com/2075-1680/12/5/496asymmetric loss functioncomposite modelsloss distributionspremium calculationrisk measures |
| spellingShingle | Enrique Calderín-Ojeda Emilio Gómez-Déniz Francisco J. Vázquez-Polo Conditional Tail Expectation and Premium Calculation under Asymmetric Loss Axioms asymmetric loss function composite models loss distributions premium calculation risk measures |
| title | Conditional Tail Expectation and Premium Calculation under Asymmetric Loss |
| title_full | Conditional Tail Expectation and Premium Calculation under Asymmetric Loss |
| title_fullStr | Conditional Tail Expectation and Premium Calculation under Asymmetric Loss |
| title_full_unstemmed | Conditional Tail Expectation and Premium Calculation under Asymmetric Loss |
| title_short | Conditional Tail Expectation and Premium Calculation under Asymmetric Loss |
| title_sort | conditional tail expectation and premium calculation under asymmetric loss |
| topic | asymmetric loss function composite models loss distributions premium calculation risk measures |
| url | https://www.mdpi.com/2075-1680/12/5/496 |
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