The Bornhuetter-Ferguson Principle

The present paper provides a unifying survey of some of the most important methods of loss reserving based on run-off triangles and proposes the use of a family of such methods instead of a single one. The starting point is the thesis that the use of run-off triangles in loss reserving can be justified only under the assumption that the de-velopment of the losses of every accident year follows a development pattern which is common to all accident years. The notion of a development pattern turns out to be a unifying force in the comparison of various methods of loss reserving, in-cluding the chain-ladder method, the loss-development method, the Cape Cod method, and the additive method. For each of these meth-ods, the predictors of the ultimate losses can be given the shape of Bornhuetter-Ferguson predictors. The process of arranging known methods of loss reserving under the umbrella of the extended Bornhuetter-Ferguson method requires the identification of prior estimators of the development pattern and the expected ultimate losses. This process can be reversed by com-bining components of different methods to obtain new versions of the extended Bornhuetter-Ferguson method. The Bornhuetter-Ferguson principle proposes the simultaneous use of various versions of the extended Bornhuetter-Ferguson method and a comparison of the resulting predictors in order to select best predictors and to determine prediction ranges