A Likelihood Approach to Bornhuetter–Ferguson Analysis

A new Bornhuetter–Ferguson method is suggested herein. This is a variant of the traditional chain ladder method. The actuary can adjust the relative ultimates using externally estimated relative ultimates. These correspond to linear constraints on the Poisson likelihood underpinning the chain ladder method. Adjusted cash flow estimates were obtained as constrained maximum likelihood estimates. The statistical derivation of the new method is provided in the generalised linear model framework. A related approach in the literature, combining unconstrained and constrained maximum likelihood estimates, is presented in the same framework and compared theoretically. A data illustration is described using a motor portfolio from a Greek insurer.This research was funded by the programme for Economic Modelling, Oxford and European Research Council, grant AdG 694262, and the Spanish Ministry of Economy and Competitiveness, grant MTM2016-76969P, which includes support from the European Regional Development Fund (ERDF)