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Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory

Published online by Cambridge University Press:  29 August 2014

Alexander J. McNeil
Alexander J. McNeil*
Affiliation:
Departement Mathematik, ETE Zentrum, CH-8092 Zürich March 7, 1997
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Abstract

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Good estimates for the tails of loss severity distributions are essential for pricing or positioning high-excess loss layers in reinsurance. We describe parametric curve-fitting methods for modelling 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 their application to Danish data on large fire insurance losses.

Keywords

Loss severity distributionshigh excess layersextreme value theoryexcesses over high thresholdsgeneralized Pareto distribution
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 27 , Issue 1 , May 1997 , pp. 117 - 137
Copyright
Copyright © International Actuarial Association 1997

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