DISCUSSION OF PAPER PUBLISHED IN VOLUME LXXXIII LOSS PREDICTION BY GENERALIZED LEAST SQUARES

In a recent paper on loss reserving, Halliwell suggests predicting outstanding claims by the method of general-ized least squares applied to a linear model. An example is the linear model given by E[Zi,k] = +®i+ °k, where Zi,k is the total claim amount of all claims which occur in year i and are settled in year i+ k. The predic-tor proposed by Halliwell is known in econometrics but it is perhaps not well-known to actuaries. The present discussion completes and simplifies the argument used by Halliwell to justify the predictor; in particular, it is shown that there is no need to consider conditional dis-tributions. 1. LOSS RESERVING For i,k! "0,1, : : :,n#, let Zi,k denote the total claim amount of all claims which occur in year i and are settled in year i+ k. We assume that the incremental claims Zi,k are observable for i+ k $ n and that they are non-observable for i+ k> n. The observable incremental claims are represented by the run-off triangle (Table 1). The non-observable incremental claims are to be predicted from the observable ones. Whether or not certain predictors ar