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Exponential dispersion models and credibility

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  • Zinoviy Landsman
  • Udi Makov

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.

Suggested Citation

  • Zinoviy Landsman & Udi Makov, 1998. "Exponential dispersion models and credibility," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1998(1), pages 89-96.
    • Handle: RePEc:taf:sactxx:v:1998:y:1998:i:1:p:89-96
    DOI: 10.1080/03461238.1998.10413995
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    Cited by:

    1. Georgios Pitselis, 2024. "Credibility Distribution Estimation with Weighted or Grouped Observations," Risks, MDPI, vol. 12(1), pages 1-27, January.

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