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.

翻译：Mack的无分布链梯法证明了链梯预测器的合理性，并使得Mack能够推导出链梯预测器条件均方预测误差的估计量。经典保险损失模型（即复合泊松型）与Mack的无分布链梯法并不一致。然而，对于一系列以暴露量（例如合同数量）为索引的复合泊松损失模型，我们证明可以通过考虑大暴露渐近性质来推导链梯预测器及Mack的条件均方预测误差估计量。因此，无需依赖无分布链梯法模型假设的有效性，即可使用Mack估计量量化链梯预测的不确定性。