Collective loss reserving with two types of claims in motor third party liability insurance

This paper adopts the new loss reserving approach proposed by Denuit and Trufin (2016), inspired from the collective model of risk theory. But instead of considering the whole set of claims as a collective, two types of claims are distinguished, those claims with relatively short development patterns and claims requiring longer developments. In each case, the total payment per cell is modelled by means of a Compound Poisson distribution with appropriate assumptions about the severities. A case study based on a motor third party liability insurance portfolio observed over 2004-2014 is used to illustrate the approach proposed in this paper. Comparisons with Chain-Ladder are performed and reveal significant differences in best estimates as well as in Value-at-Risk at high probability levels.