  The distribution-free chain ladder of Mack justified the use of the chain
ladder predictor and enabled Mack to derive an estimator of conditional mean
squared error of prediction for the chain ladder predictor. Classical insurance
loss models, i.e. of compound Poisson type, are not consistent with Mack's
distribution-free chain ladder. However, for a sequence of compound Poisson
loss models indexed by exposure (e.g. number of contracts), we show that the
chain ladder predictor and Mack's estimator of conditional mean squared error
of prediction can be derived by considering large exposure asymptotics. Hence,
quantifying chain ladder prediction uncertainty can be done with Mack's
estimator without relying on the validity of the model assumptions of the
distribution-free chain ladder.
