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Prediction error in the overdispersed Poisson model for loss development triangles. (Prognosefehler im overdispersed Poisson Modell für Abwicklungsdreiecke.) (German. English summary) Zbl 1205.91089

Summary: Two simple analytic formulas for the prediction error and the variance of the claims development result in the overdispersed Poisson model for loss development triangles are derived. The formula for the prediction error is the analog to the well known formula of Mack for the mean squared error of prediction in his chain ladder model. The formula for the variance of the claims development result is the analog to the results of Merz and Wüthrich (2008). The transpose-invariance property, mentioned by Barnett, Zehnwirth and Dubossarsky (2005), for the overdispersed Poisson model applies not only to the forecast, but of course also to prediction error and claims development result, as is shown by our symmetric formulas.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

[1] Barnett G, Zehnwirth B, Dubossarsky E (2005) When can accident years be regarded as development years? In: CAS proceedings, Bd XCII, S 239–256
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