Open Access
June 2016 Multilevel modeling of insurance claims using copulas
Peng Shi, Xiaoping Feng, Jean-Philippe Boucher
Ann. Appl. Stat. 10(2): 834-863 (June 2016). DOI: 10.1214/16-AOAS914


In property-casualty insurance, claims management is featured with the modeling of a semi-continuous insurance cost associated with individual risk transfer. This practice is further complicated by the multilevel structure of the insurance claims data, where a contract often contains a group of policyholders, each policyholder is insured under multiple types of coverage, and the contract is repeatedly observed over time. The data hierarchy introduces a complex dependence structure among claims and leads to diversification in the insurer’s liability portfolio.

To capture the unique features of policy-level insurance costs, we propose a copula regression for the multivariate longitudinal claims. In the model, the Tweedie double generalized linear model is employed to examine the semi-continuous claim cost of each coverage type, and a Gaussian copula is specified to accommodate the cross-sectional and temporal dependence among the multilevel claims. Estimation and inference is based on the composite likelihood approach and the properties of parameter estimates are investigated through simulation studies. When applied to a portfolio of personal automobile policies from a Canadian insurer, we show that the proposed copula model provides valuable insights to an insurer’s claims management process.


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Peng Shi. Xiaoping Feng. Jean-Philippe Boucher. "Multilevel modeling of insurance claims using copulas." Ann. Appl. Stat. 10 (2) 834 - 863, June 2016.


Received: 1 June 2015; Revised: 1 December 2015; Published: June 2016
First available in Project Euclid: 22 July 2016

zbMATH: 06625671
MathSciNet: MR3528362
Digital Object Identifier: 10.1214/16-AOAS914

Keywords: Composite likelihood , insurance claims , longitudinal data , multivariate regression , property-casualty insurance , Tweedie distribution

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 2 • June 2016
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