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March 2018 Extreme value modelling of water-related insurance claims
Christian Rohrbeck, Emma F. Eastoe, Arnoldo Frigessi, Jonathan A. Tawn
Ann. Appl. Stat. 12(1): 246-282 (March 2018). DOI: 10.1214/17-AOAS1081

Abstract

This paper considers the dependence between weather events, for example, rainfall or snow-melt, and the number of water-related property insurance claims. Weather events which cause severe damages are of general interest; decision makers want to take efficient actions against them while the insurance companies want to set adequate premiums. The modelling is challenging since the underlying dynamics vary across geographical regions due to differences in topology, construction designs and climate. We develop new methodology to improve the existing models which fail to model high numbers of claims. The statistical framework is based on both mixture and extremal mixture modelling, with the latter being based on a discretized generalized Pareto distribution. Furthermore, we propose a temporal clustering algorithm and derive new covariates which lead to a better understanding of the association between claims and weather events. The modelling of the claims, conditional on the locally observed weather events, both fit the marginal distributions well and capture the spatial dependence between locations. Our methodology is applied to three cities across Norway to demonstrate its benefits.

Citation

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Christian Rohrbeck. Emma F. Eastoe. Arnoldo Frigessi. Jonathan A. Tawn. "Extreme value modelling of water-related insurance claims." Ann. Appl. Stat. 12 (1) 246 - 282, March 2018. https://doi.org/10.1214/17-AOAS1081

Information

Received: 1 April 2017; Revised: 1 June 2017; Published: March 2018
First available in Project Euclid: 9 March 2018

zbMATH: 06894706
MathSciNet: MR3773393
Digital Object Identifier: 10.1214/17-AOAS1081

Keywords: Extremal dependence , extremal mixture , insurance claims , mixture modelling , Poisson hurdle model , spatio-temporal modelling

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.12 • No. 1 • March 2018
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