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 development 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, including the chain-ladder method, the loss-development method, the Cape Cod method, and the additive method. For each of these methods, 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 combining 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.