Separation of small and large claims on the basis of collective models

Abstract

This paper is inspired by two papers of Riegel who proposed to consider the paid and incurred loss development of the individual claims and to use a filter in order to separate small and large claims and to construct loss development squares for the paid or incurred small or large claims and for the numbers of large claims. We show that such loss development squares can be constructed from collective models for the accident years. Moreover, under certain assumptions on these collective models, we show that a development pattern exists for each of these loss development squares, which implies that various methods of loss reserving can be used for prediction and that the chain ladder method is a natural method for the prediction of future numbers of large claims.

Keywords:

• Loss reserving
• IBNR
• separation of small and large claims
• collective model
• development pattern

Acknowledgements

The authors are most grateful to Ulrich Riegel and an anonymous referee for several comments which helped to improve this paper.

Notes

No potential conflict of interest was reported by the authors.