The Annals of Applied Statistics

Multilevel modeling of insurance claims using copulas

Peng Shi, Xiaoping Feng, and Jean-Philippe Boucher

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Stat., Volume 10, Number 2 (2016), 834-863.

Dates
Received: June 2015
Revised: December 2015
First available in Project Euclid: 22 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1469199895

Digital Object Identifier
doi:10.1214/16-AOAS914

Mathematical Reviews number (MathSciNet)
MR3528362

Zentralblatt MATH identifier
06625671

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

Citation

Shi, Peng; Feng, Xiaoping; Boucher, Jean-Philippe. Multilevel modeling of insurance claims using copulas. Ann. Appl. Stat. 10 (2016), no. 2, 834--863. doi:10.1214/16-AOAS914. https://projecteuclid.org/euclid.aoas/1469199895


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