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

Abstract

The split credibility has been used in practice for several decades, though the foundational theory of split credibility was only investigated recently. This paper intends to study the properties of the primary loss and the excess loss in NCCI's split experience plan. We first re-visit the 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 where the frequency distribution is Poisson. We also show that the primary loss is less volatile than the total loss. Next, we show that the previously established ordering of the CV's 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.

Keywords: Workers compensation, credibility theory, split point, state limit, coefficient of variation, total loss, covariance, correlation coefficient, collective risk model

JEL Classification: C60, G22