Credibility evaluation for the exponential dispersion family

It has long been established that under regularity conditions, the Linear c redibility formula with an appropriate credibility factor produces exact fa ir premium for claims or losses whose distribution is a member of the natur al exponential family. Recently, this result has been extended to a richer family of distribution, the exponential dispersion family which comprised o f several distributions, some of which are heavy-tailed and as such could b e of significant relevance to actuarial science. The family draws its richn ess from a dispersion parameter sigma(2) = 1/lambda which is equal to 1 in the case of the natural exponential family. In this paper neither lambda is regarded known, nor a fully specified prior distribution for lambda is ass umed. Instead, by establishing a link between the m.s.e. of the linear cred ibility and Fisher information we derive optimal credibility for the case w here only the mean and variance of A are specified. (C) 1999 Elsevier Scien ce B.V. All rights reserved.