Dispersion Modelling of Outstanding Claims With Double Poisson Regression Models

Abstract

We propose a double Poisson claims reserving model with a flexible dispersion structure. The over-dispersed Poisson model is a special case of our proposed model. The maximum likelihood estimates (MLE) of mean coefficients and the residual maximum likelihood (REML) estimates of dispersion coefficients are obtained by the method of scoring. We derive the prediction error for both the incurred but not reported (IBNR) claims of each accident year and the total IBNR claims. By a quasi-likelihood approach, the proposed scoring method can be applied to non-integer or negative incremental claims. The empirical studies show that our proposed model provides a more reasonable result than the over-dispersed Poisson model.