Robust Bayesian estimation of insurance premium in collective risk model
Selected contents from this journal
Languages of publication
The collective risk model for the insurance claims is considered. The objective is to estimate a premium which is defined as a functional H specified up to an unknown parameter 'theta' (the expected number of claims). Four principles of calculating a premium are applied: net, variance principle, Esscher and exponential. The Bayesian methodology, which combines the prior knowledge about a parameter 'theta' with the knowledge in the form of a random sample, is adopted. Two loss functions (the square loss function and the asymmetric loss function LINEX) are considered. The obtained Bayes premium depends on a choice of a prior. Some uncertainty about a prior is assumed by introducing four classes of priors. The oscillation of the Bayes estimator is calculated. Considering one of the concepts of robust procedures the posterior regret 'Gamma' -minimax premiums are calculated as optimal robust premiums. A numerical example is presented.
Publication order reference
CEJSH db identifier