Credibility evaluation for the exponential dispersion family. (English) Zbl 0927.62109

Summary: It has long been established that under regularity conditions, the linear credibility formula with an appropriate credibility factor produces exact fair premium for claims or losses whose distribution is a member of the natural exponential family. Recently, this result has been extended to a richer family of distributions, the exponential dispersion family which comprised of several distributions, some of which are heavy-tailed and as such could be of significant relevance to actuarial science. The family draws its richness from a dispersion parameter \(\sigma^2=1/\lambda\) which is equal to 1 in the case of the natural exponentially family. In this paper neither \(\lambda\) is regarded known, nor a fully specified prior distribution for \(\lambda\) is assumed. Instead, by establishing a link between the m.s.e of the linear credibility and Fisher information we derive optimal credibility for the case where only the mean and variance of \(\lambda\) are specified.


62P05 Applications of statistics to actuarial sciences and financial mathematics
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