Nonparametric analysis of aggregate loss models

Abstract

This paper describes a nonparametric approach to make inferences for aggregate loss models in the insurance framework. We assume that an insurance company provides a historical sample of claims given by claim occurrence times and claim sizes. Furthermore, information may be incomplete as claims may be censored and/or truncated. In this context, the main goal of this work consists of fitting a probability model for the total amount that will be paid on all claims during a fixed future time period. In order to solve this prediction problem, we propose a new methodology based on nonparametric estimators for the density functions with censored and truncated data, the use of Monte Carlo simulation methods and bootstrap resampling. The developed methodology is useful to compare alternative pricing strategies in different insurance decision problems. The proposed procedure is illustrated with a real dataset provided by the insurance department of an international commercial company.

Keywords:

• aggregate loss models
• kernel estimator
• Monte Carlo method
• bootstrap
• censored and truncated claims

Acknowledgements

The authors would like to thank three anonymous referees for their valuable comments that helped to improve the quality of this paper. C. González-Fragueiro partially supported by the MEC Grants (ERDF included) MTM2008-00166 and SEJ2004-03303 and Xunta de Galicia 07SIN012105PR and Isidro Parga Pondal Programme.