Estimating IBNR claim counts using different levels of data aggregation

Abstract

Reserving problem in non-life insurance is an applied statistical problem with several computational aspects. In the literature, the focus has mainly been on aggregate reserving techniques and the chain-ladder method with its extensions has remained as the most widely applied claim reserving method. The classical chain-ladder method is regularly applied to annual data, but the question arises whether the reserve estimates based on more refined data outperform results obtained by annual data. We investigate whether and how much different data aggregation levels can improve the reserving process. To compare the performance of the classical chain-ladder method and its novel continuous extension, we conduct two simulation studies as well as a case study with an insurance data and use both models to estimate the IBNR claim count estimates on different levels of data aggregation. The results demonstrate that the continuous approach of the chain-ladder method provides in general a minor improvement in the IBNR predictions but proves to hold its predictive power on different types of data. This study highlights data aggregation levels in which the estimates of classical chain-ladder model outperforms the estimates obtained by the use of annual data, providing more insights for establishing accurate loss reserves.

Keywords:

• Chain-ladder method
• continuous chain-ladder
• claims reserving
• IBNR claims
• density estimation
• kernel smoothing
• predictive modeling

Acknowledgments

The authors would like to thank Katrien Antonio for providing the insurance data for the study and Roel Verbelen for constructive discussions and comments on the earlier draft of the paper.

Additional information

Funding

The research was supported by institutional research funding IUT34-5 of the Estonian Ministry of Education and Research.