Parameter Uncertainty in the Collective Risk Model

This paper proposes a new version of the collective risk model that allows for uncertainty in selecting the expected number of claims and the claim severity distribution. We provide two different methods of estimating the parameters of this model. It is demonstrated by computer simulation that one must combine the experience of several insureds in order to accurately quantify parameter uncertainty. Tests on a very large sample of individual insured data show a significant improvement in the accuracy of the collective risk model when parameter uncertainty is taken into account. The tests do not show perfect agreement between the model and the empirical data, but the agreement is close enough to be useful in many applications.