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- Publisher
- Wiley
- Copyright
- Copyright © 2006 John Wiley & Sons, Ltd.
- ISSN
- 1524-1904
- eISSN
- 1526-4025
- DOI
- 10.1002/asmb.625
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Applied Stochastic Models in Business and Industry – Wiley
Published: Mar 1, 2006