Estimating Between Line Correlations Generated by Parameter Uncertainty

When applying the collective risk model to an analysis of insurer capital needs, it is crucial to consider the effect of correlation between lines of insurance. Recent work sponsored by the Committee on the Theory of Risk has sparked the development of methods that include correlation in the collective risk model. One of these methods is built around the view that correlation is generated by parameter uncertainty affecting several lines of insurance simultaneously. This paper uses simulation analyses to explore the properties of both classical and Bayesian methods of quantifying parameter uncertainty. We conclude that in order to get sufficient accuracy to determine the necessary capital, one must use the combined data of several insurers. Using the combined data of several insurers forces us to consider a collective risk model where parameter uncertainty affects several insurers - as well as several lines of insurance - simultaneously.