Exponential dispersion models and credibility

Zinoviy Landsman and Udi Makov

Scandinavian Actuarial Journal, 1998, vol. 1998, issue 1, 89-96

Abstract: The Exponential Dispersion Family is a rich family of distributions, 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 σ2 = 1/λ which is equal to 1 in the case of the Natural Exponential Family. We consider three cases. In the first λ is assumed known, in the second a prior distribution for λ is given, and in the third the prior distribution of λ is not known and is derived by means of the maximum entropy principle, assuming the prior mean of λ can be specified. For these cases, a conjugate prior distribution for the risk parameter is assumed and credibility formulae are derived for the estimation of the fair premium.

Date: 1998
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DOI: 10.1080/03461238.1998.10413995

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