The Credibility of the Pure Premium [Discussion]

In their paper, the authors present a distribution-free approach to the problem of evaluating the full credibility standard for a specific block of business, after having briefly reviewed the customary approach. Their motivation stems from two principal concerns: (i) the usual derivation is based on the distribution of the number of claims and, generally, ignores the distribution of claim amounts even though the results are applied to such loss statistics as pure premiums and loss ratios, in addition to claim frequencies; and (ii) the third and higher moments of these distributions are usually glossed over and simply accounted for by means of a normal approximation. The results derived in the paper reaffirm the fact that the effect of (i) is very substantial, and establish that the importance of (ii) is relatively minor.