Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models
Despite the widespread use of chain-ladder models, so far no theory was available to test for model specification. The popular over-dispersed Poisson model assumes that the over-dispersion is common across the data. A further assumption is that accident year effects do not vary across development ye...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-03-01
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| Series: | Risks |
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| Online Access: | http://www.mdpi.com/2227-9091/6/2/25 |
| Summary: | Despite the widespread use of chain-ladder models, so far no theory was available to test for model specification. The popular over-dispersed Poisson model assumes that the over-dispersion is common across the data. A further assumption is that accident year effects do not vary across development years and vice versa. The log-normal chain-ladder model makes similar assumptions. We show that these assumptions can easily be tested and that similar tests can be used in both models. The tests can be implemented in a spreadsheet. We illustrate the implementation in several empirical applications. While the results for the log-normal model are valid in finite samples, those for the over-dispersed Poisson model are derived for large cell mean asymptotics which hold the number of cells fixed. We show in a simulation study that the finite sample performance is close to the asymptotic performance. |
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| ISSN: | 2227-9091 |