Credibility theory: a new view from the theory of second order optimal statistics

Second order (s.o.) Bayes estimators, being the main tool in the s.o. optimal statistical theory, provides a natural basis for a new approach to credibility evaluation. For the cases, where the classical credibility formula fails in the sense that it does no longer represent the predicted mean, this approach suggests an s.o. modified credibility formula, which approximately (in some sense) equals the predicted mean even for small size samples. The results are applied to the important class of location dispersion distributions and are illustrated by a number of numerical experiments.