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Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models

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  • Jonas Harnau

    (Department of Economics, University of Oxford & Oriel College, Oxford OX1 4EW, UK)

Abstract

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.

Suggested Citation

  • Jonas Harnau, 2018. "Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models," Risks, MDPI, vol. 6(2), pages 1-25, March.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:25-:d:137814
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    References listed on IDEAS

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    Cited by:

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