Credibility theory is the adaptation of theoretical statistics to a variety of daily business problems.It illustrates the actuarial perspective.
Credibility theory is one of the first and most productive fields of actuarial work. Almost every decade, it gets reinvigorated with new techniques with new implications on pricing and valuations. Even today, the theory of credibility has several untested aspects, waiting to be validated.
The statistician can measure confidence intervals, telling us when we may be 95% correct in our estimation, but we are rarely so sure of our estimates, or even if we are, we do not need then need actuaries.
However, the actuaries then tells us to join our confidence in the data with other information and business considerations. The credibility theory has come a long way, from the earliest models of classical through the convergence of credibility theory with the Bayesian analysis:
- At one time it was considered that the classical theory and Bayesian-Buhlmann credibility were competing theories, and the latter would ultimately replace the older one. Gary Venter, showed that the two credibility traditions had different objectives, classical credibility sought to minimize rate fluctuations whereas Bayesian-Buhlmann credibility sought to optimize pricing accuracy.
- Over time, credibility theory has undergone many changes. Howard Mahler, one of the leading actuarial authors, showed how credibility varied with the extent to which risk parameters shifted over time.
Mahler has changed many of the previous actuarial notions of credibility. Firstly, the speed at which the risk parameters shift is not less important than the volume of business for setting credibility values. Secondly, he showed that there is quite a large range of optimal credibility values.
Any value chosen from this range works equally well for maximizing pricing accuracy. However, the actuary should examine the rate at which the risk parameters shift to determine whether older experience years have much predictive value for the future. Thirdly, though credibility theory was nourished by casualty actuaries, it is now being used in other fields like financial engineering too. Actuaries estimate loss frequency and loss severity, whereas financial engineers estimate betas and volatility.