A posteriori ratemaking using bivariate Poisson models

Abstract

Recently, different bivariate Poisson regression models have been used in the actuarial literature to make an a priori ratemaking taking into account the dependence between two types of claims. A natural extension for these models is to consider a posteriori ratemaking (i.e. experience rating models) that also relaxes the independence assumption. We introduce here two bivariate experience rating models that integrate the a priori ratemaking based on the bivariate Poisson regression models, extending the existing literature for the univariate case to the bivariate case. These bivariate experience rating models are applied to an automobile insurance claims data-set to analyse the consequences for posterior premiums when the independence assumption is relaxed. The main finding is that the a posteriori risk factors obtained with the bivariate experience rating models are significantly lower than those factors derived under the independence assumption.

Keywords:

• bivariate Poisson regression models
• automobile insu rance
• experience rating models
• Bayesian approach

Acknowledgements

The authors wish to acknowledge discussions with researchers at Riskcenter at the University of Barcelona.

Notes

No potential conflict of interest was reported by the authors.

1 Assuming the amount of the expected claims equals one monetary unit, for both types of claims.

Additional information

Funding

This work was supported by the Spanish Ministry of Economy [grant number ECO2012-35584].