A Bayesian analysis of clusters of extreme losses

Occasional short range dependence in a claim generating process, probably induced by some subordinated process, may result in clusters of extreme losses. Under such circumstances, the iid assumption for the exceedances may not hold anymore. For a given value of the retention level, we overcome this...

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Bibliographic Details
Published in:Applied stochastic models in business and industry 2006-03, Vol.22 (2), p.155-167
Main Author: Vaz de Melo Mendes, Beatriz
Format: Article
Language:English
Subjects:
Bayesian analysis
cluster of extremes
excess of loss
extreme value theory
reinsurance
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Summary:Occasional short range dependence in a claim generating process, probably induced by some subordinated process, may result in clusters of extreme losses. Under such circumstances, the iid assumption for the exceedances may not hold anymore. For a given value of the retention level, we overcome this difficulty by applying an empirical rule for cluster definition and aggregating the excesses within clusters. This modelling strategy is compared to the classical random sum of excess losses model based on the iid assumption. The usual discrete probability models and an extreme value distribution from the Pareto family are assumed, respectively, for the counting processes and the severities. Bayesian techniques are then used to obtain a predictive distribution of the annual excess claim amount. Maximum likelihood estimates are also computed and compared. We illustrate using a fire insurance claims data. The Bayesian approach provided more conservative point and interval estimates for the statistical premium. Copyright © 2006 John Wiley & Sons, Ltd.
ISSN:1524-1904
1526-4025
DOI:10.1002/asmb.625