Credibility With Shifting Risk Parameters, Risk Heterogeneity, and Parameter Uncertainty

This paper explores the important effects on credibility of three phenomena: shifting risk parameters, risk heterogeneity, and parameter uncertainty. When any of these phenomena are significant, the Buhlmann credibility formula no longer applies. Covariance structures corresponding to these phenomena both separately and in combination are shown. Linear equations for the corresponding credibilities are derived. Possible applications to classification ratemaking, overall rate indication calculation, and experience rating are illustrated in detail. The procedure for estimating the parameters of the covariance structure is discussed for each situation. Illustrative credibilities are then calculated for each situation.