Double chain ladder, claims development inflation and zero-claims

Abstract

Double chain ladder demonstrated how the classical chain ladder technique can be broken down into separate components. It was shown that under certain model assumptions and via one particular estimation technique, it is possible to interpret the classical chain ladder method as a model of the observed number of counts with a built-in delay function from when a claim is reported until it is paid. In this paper, we investigate the double chain ladder model further and consider the case when other knowledge is available, focusing on two specific types of prior knowledge, namely prior knowledge on the number of zero-claims for each underwriting year and prior knowledge about the relationship between the development of the claim and its mean severity. Both types of prior knowledge readily lend themselves to be included in the double chain ladder framework.

Keywords:

• prior knowledge
• claims reserves
• reserve risk
• over-dispersed poisson model
• cash flow
• bootstrap

Acknowledgments

This research was financially supported by a pump-priming grant by the Actuarial Profession. The first author is also supported by the Spanish Ministerio de Ciencia e Innovación, Project MTM2008-03010 and the European Commission under the Marie Curie Intra-European Fellowship FP7-PEOPLE-2011-IEF Project number 302600. All the calculations in the paper were performed in R (R Development Core Team 2011). R-scripts to reproduce the results in this paper are available on request by email to the authors.