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 conjugate. When the claim size follows a distribution outside this family, the credibility formula offers an inaccurate estimation of the mean future claim. The established analogy between the credibility formula and stochastic approximation [Landsman, Z., Makov, U., 1999. On Stochastic Approximation and Credibility. Scand. Actuarial J., to appear] offers a way of devising credibility estimation for distributions other than members of the EDF. In this paper we suggest sequential credibility estimators which are suited to deal with distributions belonging to the symmetric location dispersion family.