The Borhuetter-Ferguson Claims Reserving Method and Generalized Linear Models

In the actuarial practice, the Bornhuetter-Ferguson (BF) method is commonly used to combine external estimates of the expected ultimate claims with data of a run-off triangle of payments. The BF claims reserve of each accident year is proportional to the external estimates. The coefficients of proportionality depend on the claims development pattern and are usually estimated by the Chain-ladder technique. Mack (2006) criticizes this solution and proposes different estimates. In this paper we tackle the problem in the framework of Generalized Linear Models (GLM), where the external estimates can be incorporated by means of offset terms. We show that a particular GLM allows obtaining the estimates of the claims development pattern suggested by Mack. Within the GLM framework we can easily calculate prediction errors to evaluate the uncertainty connected with the estimates of the claims development pattern. By simulation we can also evaluate the uncertainty due to the external estimate of the ultimate claims.