Principles and Application of Credibility Theory

We review the history of the practical development of credibility theory. Emphasis is placed on the two main approaches to credibility theory: limited fluctuation credibility and greatest accuracy credibility. We explain when each approach should and should not be used. The presentation of greatest accuracy credibility theory starts with a review of (exact) Bayesian credibility and then moves to the Buhlmann-Straub model. Estimators of the structure parameters are discussed. Examples are presented to illustrate the concepts. Finally, the hierarchical credibility and crossed classification credibility models are presented