Quantifying the Uncertainty in Claim Severity Estimates for an Excess Layer When Using the Single Parameter Pareto

This paper addresses the question: How valuable is a sample of excess claims in determining the expected claim severity in an excess layer of insurance? An established procedure to estimate this expected claim severity is to first fit a model distribution to claim size data and then, using the fitted distribution, estimate the expected claim severity in the given excess layer. One of the more popular models used is the single parameter Pareto. This paper provides a mean of quantifying the uncertainty in these excess claim severity estimates when using the single parameter Pareto. This approach requires one to incorporate prior opinions about the distribution of the Pareto parameter using Bayes’ Theorem. Reinsurance Research - Loss Distributions, Size of