The Doubler Chain Ladder and its extensions

Specialeforsvar ved Teis Schneider Dengsøe 

Titel: The Doubler Chain Ladder and its extensions

Abstract: For decades actuaries have used methods such as the Chain Ladder method and the Bornhuetter- Ferguson method to calculate reserves. These methods are relatively easy to understand and have been implemented in insurance companies around the world, across various business lines. The historical data used in these methods are typically the number of accidents reported or the size of the payments made by the insurance company, commonly presented in a counts triangle or a payments triangle. This thesis introduces the reserving technique known as the Double Chain Ladder method. Papers by Martinez, Nielsen et al. builds on the idea of combining the claim numbers and the total claims triangle to take advantage of the information in both of them. The overall idea is to apply the Chain Ladder method twice, on two different triangles. This leaves us with more parameters to estimate, than we are used to in the classical Chain Ladder method. However, it allows us to model the reporting delay and the settlement delay and to split up the estimate of the total outstanding claims in an RBNS part and an IBNR part. Various versions and extensions to the Double Chain Ladder method are examined. Some exten-sions are statistical models only relying on first order moment assumptions, whereas other extensions involve additional distributional properties. Furthermore, introducing a third triangle containing expert knowledge from the claims department in the form of an incurred triangle, leads to additional models, dealing with the volatility that generally comes with paid dat. Some of the models merely replicate the reserves from the classical Chain Ladder method, but all models provide us with full cash flows and divide reserves into RBNS/IBNR reserves, a feature which the classical Chain Ladder method lacks. The models are tested and validated on motor liability data from an actual insurance portfolio, and a bootstrap algorithm for the RBNS, IBNR and total reserves is incorporated. We conclude that the incorporation of expert knowledge has the largest effect on the reserve levels, based on data from the examined insurance portfolio. This supports the rationale for using incurred data in reserving departments

 Vejledere:  Jostein Paulsen
                   Tine Buch-Kromann, Tryg
Censor:       Mette M Havning