Provisions for Outstanding Claims with Distance-Based Generalized Linear Models

In previous works we developed the formulas of the prediction error in generalized linear model (GLM) for the future payments by calendar years assuming the logarithmic link and the parametric family of error distributions named power family. In the particular case of assuming (overdispersed) Poisson and logarithmic link the GLM gives the same provision estimations as those of the Chain-Ladder deterministic method. Now, we are studying the possibility to use distance-based generalized linear models (DB-GLM) to solve the problem of claim reserving in the same way as GLM is used in this context. DB-GLM can be fitted by using the function dbglm of the dbstats package for R. In this study we calculate the prediction error associated to the accident years future payments and total payment, and also to the calendar years future payments using DB-GLM in the general case of the power families of error distributions and link functions. We make an application with the well known run-off triangle of Taylor and Ashe.