Pure robust versus robust portfolio unbiased—Credibility and asymptotic optimality

Empirical credibility estimation, which is a credibility counterpart of empirical Bayes estimation, lacks robustness due to the sensitivity of estimators to outlier events. In this paper we combine robust statistics with empirical linear Bayes estimation and derive robust asymptotic optimality based on Norberg’s (1980) proposal. Robust portfolio-unbiased empirical regression credibility is derived and its asymptotic optimality is proved, under not very restrictive assumptions. The asymptotic optimality of pure robust credibility estimators is also proved. The superiority of the pure robust credibility estimation against the robust portfolio-unbiased credibility estimation is presented and verified with numerical results.