Unbiased estimator for the ultimate claim prediction error in the chain-ladder model of Mack

Abstract

We propose a new estimator for the ultimate prediction uncertainty within the famous Mack’s distribution-free chain-ladder model, which can be proved to be unbiased (conditionally given the first triangle column) under some additional technical assumptions. A peculiar behaviour of the unbiased estimator is given by its possible negativity. This is a drawback which might be worth trading off for the unbiasedness property, since there is empirical evidence that the likelihood of a negative realisation is extremely low. This offers an alternative to the well-known Mack and BBMW formulas since the latters can be proved to be biased. However, we also show that this novel estimator, as well as the Mack and BBMW formulas, can (with non-negligible probability) materially fail to estimate the true uncertainty.