Sequential credibility evaluation for symmetric location claim distributions

The traditional linear credibility formula provides an exact expression for the predictive mean when the conditional loss distributions belong to the exponential dispersion family (EDF) and when the prior distribution is conj ugate. When the claim size follows a distribution outside this family, the credibility formula offers an inaccurate estimation of the mean future clai m. The established analogy between the credibility formula and stochastic a pproximation [Landsman, Z., Makov, U., 1999. On Stochastic Approximation an d Credibility. Scand. Actuarial J., to appear] offers a way of devising cre dibility estimation for distributions other than members of the EDF. In thi s paper we suggest sequential credibility estimators which are suited to de al with distributions belonging to the symmetric location dispersion family . (C) 1999 Elsevier Science B.V. All rights reserved.