A Class of Conjugate Priors with Applications to Excess-of-Loss Reinsurance

We consider the problem of forecasting the total cost of claims in excess-of-loss reinsurance. The number of claims reported to the direct insurer is assumed to follow a Poisson law, and the claim severities are modelled by a Pareto distribution. The Poisson frequency as well as the Pareto parameter will be considered as random parameters in a Bayesian setting. We derive the class of conjugate joint prior distributions, which turn out to specify a (prior) dependence between the two parameters. The use of conjugate prior facilitates the mathematical analysis, and it also makes it easy to interpret the parameters of the prior distribution. Reinsurance Research - Loss Distributions, Size of