Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

Abstract The article presents a collective risk model for the insurance claims. objective is to estimate premium, which defined as functional specified up unknown parameters. For this purpose, Bayesian methodology, combines prior knowledge about certain parameters with in form of random sample, has been adopted. generalised Bregman loss function considered. In effect, results can be applied numerous functions, including square-error, LINEX, weighted Brown, entropy loss. Some uncertainty assumed by distorted band class priors. range and Bayes premiums calculated posterior regret Γ-minimax premium robust procedure implemented. Two examples are provided illustrate issues considered - first one an parameter Poisson distribution, second distributions number severity