A Comparison of Stochastic Models that Reproduce Chainladder Reserve Estimates

It is shown that the (over-dispersed) Poisson model is not the same as the distribution-free chain ladder model of Mack (Distribution-free calculation of the standard error of chain ladder reserve estimates, ASTIN Bulletin 23 (1993) 213--225) although both reproduce the historical chain ladder estimator for the claims reserve. For example, the true expected claims reserves, ignoring estimation issues, described by the two models are different. Moreover, the Poisson model deviates from the historical chain ladder algorithm in several aspects that the distribution-free chain ladder model does not. Therefore, only the latter can qualify to be referred to as the model underlying the chain ladder algorithm.