Modeling claims data with composite Stoppa models

Abstract

In this paper, a new class of composite model is proposed for modeling actuarial claims data of mixed sizes. The model is developed using the Stoppa distribution and a mode-matching procedure. The use of the Stoppa distribution allows for more flexibility over the thickness of the tail, and the mode-matching procedure gives a simple derivation of the model compositing with a variety of distributions. In particular, the Weibull–Stoppa and the Lognormal–Stoppa distributions are investigated. Their performance is compared with existing composite models in the context of the well-known Danish fire insurance data-set. The results suggest the composite Weibull–Stoppa model outperforms the existing composite models in all seven goodness-of-fit measures considered.

Keywords:

• Stoppa distribution
• Lognormal distribution
• Weibull distribution
• Danish fire losses
• spliced model
• goodness-of-fit
• composite model
• bootstrap

Acknowledgements

The authors would like to express their gratitude to an anonymous referee for the relevant and useful comments that have improved this paper. This paper was supported by The University of Melbourne ECR Grant Scheme.

Disclosure statement

No potential conflict of interest was reported by the authors.