Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory

Good estimates for the tails of loss severity distributions are essential for pricing or positioning high-excess loss layers m reinsurance We describe parametric curvefitting methods for modeling extreme historical losses These methods revolve around the generalized Pareto distribution and are supported by extreme value theory. We summarize relevant theoretical results and provide an extensive example of the application to Danish data on large fire insurance losses.