Discussion on “q-Credibility” by Olivier Le Courtois

The classical credibility theory circumvents the challenge of finding the bona fide Bayesian estimate (with respect to the square loss) by restricting attention to the class of linear estimators of data. See, for example, Bühlmann and Gisler (2005) and Klugman et al. (2008) for a detailed treatment. Though it is simple to implement and easy to interpret, the classical credibility theory basically only guarantees accurate estimation (i.e., exact credibility) under fairly restricted assumptions such as exponential family models with conjugate priors (Diaconis and Ylvisaker 1979). Therefore, it is natural to seek alternative and more general methods for estimating the mean loss. One such approach is to consider the best quadratic estimator of data, as Dr. Le Courtois has done with his q-credibility proposal. In this note we provide three comments. The first shows how Le Courtois’s Proposition 1.1 can be simultaneously extended and the proof simplified; the second discusses what actuaries can do beyond the classical credibility theory; and the third poses several open problems.