On the use of posterior regret Gamma-minimax actions to obtain credibility premiums

Abstract

Computing premiums in a Bayesian context requires the use of a prior distribution that the unknown risk parameter follows in the heterogeneous portfolio. Following the methodology that an actuary only has vague information about this parameter and therefore is unable to specify a simple prior, we choose a class Γ of priors and compute posterior regret Γ-minimax premiums which can be written, under appropriate likelihoods and priors, as a credibility formula.