Exponential dispersion models and credibility
- 1 January 1998
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1998 (1) , 89-96
- https://doi.org/10.1080/03461238.1998.10413995
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 σ 2 = 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.Keywords
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