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Erscheinungsjahr: 
2018
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 6 [Issue:] 3 [Publisher:] MDPI [Place:] Basel [Year:] 2018 [Pages:] 1-37
Verlag: 
MDPI, Basel
Zusammenfassung: 
Although both over-dispersed Poisson and log-normal chain-ladder models are popular in claim reserving, it is not obvious when to choose which model. Yet, the two models are obviously different. While the over-dispersed Poisson model imposes the variance to mean ratio to be common across the array, the log-normal model assumes the same for the standard deviation to mean ratio. Leveraging this insight, we propose a test that has the power to distinguish between the two models. The theory is asymptotic, but it does not build on a large size of the array and, instead, makes use of information accumulating within the cells. The test has a non-standard asymptotic distribution; however, saddle point approximations are available. We show in a simulation study that these approximations are accurate and that the test performs well in finite samples and has high power.
Schlagwörter: 
non-nested testing
encompassing
chain-ladder
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