On the Properties of the Primary Loss and the Excess Loss in NCCI’s Experience Rating Plan

Split credibility has been used in practice for several decades, though its foundational theory has been investigated only recently. This paper studies the properties of the primary loss and the excess loss in the split experience plan of the National Council on Compensation Insurance (NCCI). We first revisit the claim that the excess loss is more volatile than the total loss. We show that this claim holds in the collective risk model with an arbitrary frequency distribution, generalizing an extant result in which the frequency distribution is a Poisson distribution. We also show that the primary loss is less volatile than the total loss. Next, we show that the previously established ordering of the coefficients of variation of the primary loss, the excess loss, and the total loss also holds in a more general model. Finally, we investigate the covariance and correlation coefficient between the primary loss and the excess loss. We also discuss some potential applications of our results. The paper concludes with some conjectures.