Claim Reserving Using Distance Based Generalized Linear Models
Generalized linear models (GLM) can be considered a stochastic version of the classical Chain Ladder (CL) method of claim reserving in nonlife insurance. In particular, the deterministic CL model is reproduced when a GLM is fitted assuming over dispersed Poisson error distribution and logarithmic link. Our aim is to propose the use of distance based generalized linear models (DB GLM) in the claim reserving problem. DB GLM can be considered a generalization of the classical GLM to the distance based analysis, because DB GLM contains as a particular instance ordinary GLM when the Euclidean, (l^2\ metric is applied. Then, DB GLM can be considered too a stochastic version of the CL claim reserving method. In DB GLM, the only information required is a predictor distance matrix. DB GLM can be fitted using the dbstats package for R. To estimate reserve distributions and standard errors, we propose a nonparametric bootstrap technique adequate to the distance based regression models. We illustrate the method with a well known actuarial dataset.