Mack's estimator motivated by large exposure asymptotics in a compound Poisson setting (Q6556602)

The article deals with the convergence (a.s. and in distribution) of certain sequences of random variables. The main results consist of Theorems 1--5. According to the abstract ``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.''