Asymptotic behaviors of stochastic reserving: Aggregate versus individual models

In this paper, we investigate the asymptotic behaviors of the loss reservings computed by individual data method and its aggregate data versions by Chain-Ladder (CL) and Bornhuetter-Ferguson (BF) algorithms. It is shown that all deviations of the three reservings from the individual loss reserve (the projection of the outstanding liability on the individual data) converge weakly to a zero-mean normal distribution at the nrate. The analytical forms of the asymptotic variances are derived and compared by both analytical and numerical examples. The results show that the individual method has the smallest asymptotic variance, followed by the BF algorithm, and the CL algorithm has the largest asymptotic variance.