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.

Markowitz optimal portfolio theory (Markowitz 1987), also known as the Mean-Variance theory, has had a tremendous impact and hundreds of papers are devoted to this topic. This theory addresses the ...

Bayesian ideas were introduced into actuarial science in the late 1960s in the form of empirical credibility methods for premium setting. The advance of the Bayesian methodology was slow due to its subjective nature and to the computational difficulties associated with the full Bayesian analysis. This paper offers a brief survey of Bayesian solutions to some actuarial problems and discusses the current state of research.