Discussion of the Mean Square Error of Prediction in the Chain-Ladder Reserving Method

For a dozen or so years the chain ladder models of Murphy and Mack have been known to give the same reserve estimates but differ slightly in their assumptions and in their calculations of the reserve variance. Up until now no one had provided a detailed analysis of the source of the difference in variance. The current (BBMW) paper shows that this arises from a slight difference in the estimates of the parameter variance piece, and this in turn comes from the fact that for Murphy the errors in the estimates of the development factors are independent, while under Mack’s assumptions they are merely uncorrelated. This would suggest that any given data could be tested for the difference in assumptions by computing correlations of functions of the estimated factors. For instance a finding that some functions of the factors are correlated but the factors themselves are uncorrelated would support Mack’s model over Murphy’s.