June 2024 Hierarchical dependence modeling for the analysis of large insurance claims data
Ting Fung Ma, Yizhou Cai, Peng Shi, Jun Zhu
Author Affiliations +
Ann. Appl. Stat. 18(2): 1404-1420 (June 2024). DOI: 10.1214/23-AOAS1840


Extreme weather events associated with climate change have caused significant damages. In particular, hail storms damage millions of properties in the U.S. and result in billion-dollar insured losses each year in the recent decade. To facilitate the insurance claims management operations in insurance companies, we construct a hierarchical dependence model, which accommodates the complex dependence within and between the outcomes of interests including the propensity of filing a claim, time to report a claim, and the claim amount. The storm-specific and property-specific characteristics are incorporated through marginal models, such as generalized linear models and survival analysis models. The dependence within the hail event is captured by spatial factor copula, while the dependence between different outcomes is captured by bivariate copula. For parameter estimation we develop a two-step procedure that first maximizes the marginal likelihood function and then maximizes the pairwise likelihood, which ensures computational feasibility for big data. We apply this modeling framework to analyze a large dataset involving hail storms in Colorado from 2011 to 2015 impacting hundreds of thousands of insured properties and demonstrate that the predictive performance can be improved by our proposed methodology.


The authors would like to thank the Editor, Associate Editor, and reviewer for many helpful comments. This material is based upon work supported by and while serving at the National Science Foundation. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.


Download Citation

Ting Fung Ma. Yizhou Cai. Peng Shi. Jun Zhu. "Hierarchical dependence modeling for the analysis of large insurance claims data." Ann. Appl. Stat. 18 (2) 1404 - 1420, June 2024. https://doi.org/10.1214/23-AOAS1840


Received: 1 January 2023; Revised: 1 October 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1840

Keywords: Composite likelihood , copula , non-Gaussian data , nonstationary process , replicated data , two-step estimation

Rights: Copyright © 2024 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.18 • No. 2 • June 2024
Back to Top