Credibility evaluation for the exponential dispersion family

✍ Scribed by Zinoviy Landsman; Udi E. Makov

• Book ID: 104300003
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 84 KB
• Volume: 24
• Category: Article
• ISSN: 0167-6687
• DOI: 10.1016/s0167-6687(98)00035-3

✦ Synopsis

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 distribution, 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 σ 2 = 1/λ which is equal to 1 in the case of the natural exponential family. In this paper neither λ is regarded known, nor a fully specified prior distribution for λ 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 λ are specified.