Fitting Tweedie's compound Poisson model to pure premium with the EM algorithm

Abstract

We consider the situation when the number of claims is unavailable, and a Tweedie's compound Poisson model is fitted to the observed pure premium. Currently, there are two different models based on the Tweedie distribution: a single generalized linear model (GLM) for mean and a double generalized linear model (DGLM) for both mean and dispersion. Although the DGLM approach facilitates the heterogeneous dispersion, its soundness relies on the accuracy of the saddlepoint approximation, which is poor when the proportion of zero claims is large. For both models, the power variance parameter is estimated by considering the profile likelihood, which is computationally expensive. We propose a new approach to fit the Tweedie model with the EM algorithm, which is equivalent to an iteratively re-weighted Poisson-gamma model on an augmented data set. The proposed approach addresses the heterogeneous dispersion without needing the saddlepoint approximation, and the power variance parameter is estimated during the model fitting. Numerical examples show that our proposed approach is superior to the two competing models.