Loss Models: From Data to Decisions, 4th Edition

18.8 Notes and References

In this section, one of the two major criticisms of limited fluctuation credibility has been addressed. Through the use of the variance of the hypothetical means, we now have a means of relating the mean of the group of interest, μ(θ), to the manual, or collective, premium, μ. The development is also mathematically sound in that the results follow directly from a specific model and objective. We have also seen that the additional restriction of a linear solution is not as bad as it might be in that we still often obtain the exact Bayesian solution. There has subsequently been a great deal of effort expended to generalize the model. With a sound basis for obtaining a credibility premium, we have but one remaining obstacle: how to numerically estimate the quantities a and v in the Bühlmann formulation, or how to specify the prior distribution in the Bayesian formulation. Those matters are addressed in Chapter 19.

A historical review of credibility theory including a description of the limited fluctuation and greatest accuracy approaches is provided by Norberg [82]. Since the classic paper of Bühlmann [17], there has developed a vast literature on credibility theory in the actuarial literature. Other elementary introductions are given by Herzog [42] and Waters [119]. Other more advanced treatments are Goovaerts and Hoogstad [39] and Sundt [ 108]. An important generalization of the Bühlmann–Straub model is the Hachemeister [40] regression model, which is not ...