An Analysis of Experience Rating

Experience rating formulas that are currently in use have features that have no counterpart in the literature on Bayesian credibility. These features include the limiting of individual losses that go into the experience rating, separate treatment of primary and excess losses, and the gradual transition to self-rating. This paper analyzes the effect of these features using the collective risk model. Most developments in Bayesian credibility assume that the variance of an individual insured's experience is inversely proportional to the size of the insured. This will not be the case if the parameters of the insured's loss distribution are changing over time. This paper analyzes the effect of this parameter uncertainty on the Bayesian credibility formulas. Finally, Paul Dorweiler's method of testing experience rating formulas is updated using modern statistical methodology. The result is a very general method of evaluating the parameters of an experience rating formula. Keywords: Credibility