Open Access
December 2024 Bayesian modeling of insurance claims for hail damage
Ophélia Miralles, Anthony C. Davison
Author Affiliations +
Ann. Appl. Stat. 18(4): 3091-3108 (December 2024). DOI: 10.1214/24-AOAS1925

Abstract

Despite its importance for insurance, there is almost no literature on statistical hail damage modeling. Statistical models for hailstorms exist, though they are generally not open-source, but no study appears to have developed a stochastic hail impact function. In this paper we use hail-related insurance claim data to build a Gaussian line process with extreme marks in order to model both the geographical footprint of a hailstorm and the damage to buildings that hailstones can cause. We build a model for the claim counts and claim values, and compare it to the use of a benchmark deterministic hail impact function. Our model proves to be better than the benchmark at capturing hail spatial patterns and allows for localized and extreme damage, which is seen in the insurance data. The evaluation of both the claim counts and value predictions shows that performance is improved compared to the benchmark, especially for extreme damage. Our model appears to be the first to provide realistic estimates for hail damage to individual buildings.

Funding Statement

Ophélia Miralles’ work was partially funded by the Swiss National Science Foundation (project 200021_178824).

Acknowledgments

We thank the Federal Office of Meteorology and Climatology (MeteoSwiss) for providing the POH and MESHS data, the insurance company GVZ for providing the building damage and exposure data, Timo Schmid from ETHZ for providing CLIMADA outputs, and Daniel Steinfeld of GVZ for valuable insights.

Citation

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Ophélia Miralles. Anthony C. Davison. "Bayesian modeling of insurance claims for hail damage." Ann. Appl. Stat. 18 (4) 3091 - 3108, December 2024. https://doi.org/10.1214/24-AOAS1925

Information

Received: 1 July 2023; Revised: 1 May 2024; Published: December 2024
First available in Project Euclid: 31 October 2024

Digital Object Identifier: 10.1214/24-AOAS1925

Keywords: Bayesian modeling , climate extremes , Extreme value analysis , hail damage , line process

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.18 • No. 4 • December 2024
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