E-Bayesian estimation and prediction of insurance premium in Poisson model

Premium estimation and prediction are widely applied in insurance, healthcare, and finance to improve risk management, pricing accuracy, and customer personalization. They help insurers balance profitability with fairness, while giving customers more transparent and tailored options. In this paper, the E-Bayesian estimation of premium and predicting the number of claims is considered when the number of claims follows a Poisson distribution. The Escher premium principle is used to obtain the estimators and predictors. The Bayesian and E-Bayesian estimators of premium are derived under three densities for hyperparameters of prior distribution and compared by using a simulation study. A real data analysis is given to illustrate the results. The method of E-Bayesian estimation is extended to E-Bayesian predicting the number of claims. Performance of the proposed predictors are evaluated conducting a prequential analysis within a simulation.