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