Imprecise Credibility Theory

Abstract

The classical credibility theory is a cornerstone of experience rating especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we take a page out of the robust Bayesian book and propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly-robust in the sense that it retains the credibility estimator's freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.

Keywords: Imprecise probability; credibility estimator; model misspecification; prior uncertainty; robustness