An Iterated Bornhuetter-Ferguson Model

Abstract

The iterated Bornhuetter-Ferguson loss reserving method generates an infinite sequence of reserve formulas, with the chain ladder and Bornhuetter-Ferguson formulas at opposite extremes. The sequence also contains the Benktander-Hovinen formula. Although the literature contains parametric stochastic models for the first two of these three, it does not contain models for the remainder of the sequence. The present paper fills this gap with a sequence of Bayesian chain ladder models, one for each iterate. Each is an ODP chain ladder model, with each row parameter drawn from a gamma prior. The parameters vary from iterate to iterate. Equality between each Bayesian chain ladder model and its corresponding iterate is achieved by suitable choice of the coefficients of variation of the row parameters. Thus, each iterate is a special case of the general Gamma-ODP model. Applications of this sequence of models are illustrated, first the application of the sequence of Bayesian chain ladder models directly to loss reserving, and second to a hierarchy of proportional reinsurance arrangements. In the first of these applications, the parameter selection for the Gamma-ODP special cases will not always be natural or intuitive. The use of the general Gamma-ODP model with more natural parameter values may be preferable.