On the Importance of Dispersion Modeling for Claims Reserving: An Application with the Tweedie Distribution
By Jean-Philippe Boucher, Danail Davidov
We consider Tweedie’s compound Poisson model in a claims reserving triangle in a generalized linear model framework. We show that there exist practical situations where the variance, as well as the mean of the costs, needs to be modeled. We optimize the likelihood function through either direct optimization or through double generalized linear models (DGLM). We also enhance the estimation of the variance parameters within the DGLM by using the restricted maximum likelihood (REML). Having a flexible variance structure allows the model to replicate the underlying risk more appropriately and shrinks the gap between the predicted variances of different models.
Keywords: Claims reserves, incurred but not reported, mean square error of prediction, Tweedie, compound Poisson model, exposure, generalized linear model, dispersion, double generalized linear model (DGLM), power variance function, restricted maximum likelihood, saddle-point approximation