Bayes, E-Bayes and Robust Bayes Premium Estimation and Prediction under the Squared Log Error Loss Function

In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfolio. When the prior knowledge is vague, the E-Bayesian and robust Bayesian analysis can be used to handle the uncertainty in specifying the prior distribution by considering a class of priors instead of a single prior. In this paper, we study the E-Bayes and robust Bayes premium estimation and prediction in exponential model under the squared log error loss function. A prequential analysis in a simulation study is carried out to compare the proposed predictors. Finally, a real data example is included for illustrating the results.