Copula based Bayesian data analysis of loss reserving

Abstract

Prediction of loss reserves corresponding to dependent lines of business is one of the most important problems in the actuarial sciences. In this paper, we propose a class of copula based multivariate distributions to model the losses with the heavy tailed distribution in the run-off triangles to predict unpaid losses. We set up ANOVA, ANCOVA, and state space models with four choices of copulas, Clayton, Frank, Gumbel, and Gaussian to provide a new procedure for analyzing run-off triangle tables. We use the Hamiltonian Monte Carlo sampler to perform a Bayesian analysis to estimate the parameters. We apply the proposed models to the data set consists of two lines of business of paid losses data from the Schedule P of the National Association of Insurance Commissioners (NAIC) database. Using some well known criteria, we compare the prediction accuracy of the mean models. As a result, the ANCOVA model with the Clayton copula dominates the other models.

Keywords:

• Archimedean copulas
• Bayesian analysis
• Hamiltonian Monte Carlo sampler
• heavy-tailed distribution
• multivariate loss reserving
• run-off triangles

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15

Acknowledgement

The authors would like to thank the anonymous reviewer for his/her valuable comments and suggestions, which definitely improved the quality and presentation of the paper.