Predictive Aggregate Claims Distributions

Abstract

In the collective risk model we use the objective Bayesian approach to calculate predictive aggregate claims distributions. Very often this is equivalent to the profile predictive likelihood approach, but the former is more straightforward to apply, and accordingly we use it as a pragmatic device. We compare the predictive distributions with fitted distributions which take no account of parameter uncertainty and show that actuarial functions such as premiums can be substantially understated if parameter uncertainty is ignored. We illustrate the situation when the moments of the predictive individual claim amount distribution do not exist and we discuss ways of applying such distributions to insurance problems.