Experience rating of risk premium for Esscher premium principle

In this article, a new method is introduced under the Bayesian framework to derive the credibility estimator of risk premiums based on the Esscher premium principle. This new estimator offers desirable statistical properties, making it more useful and practical compared to existing estimators. Additionally, Bayesian models for policy portfolios are established, and empirical Bayes methods are employed to estimate the structural parameters. The empirical Bayesian estimation of risk premiums is also discussed in detail. The convergence rate and goodness of the proposed estimators are verified through simulations. The results demonstrate the effectiveness and accuracy of the new estimator and its superior performance compared to other existing methods. Finally, an empirical analysis is conducted using real insurance data, which further confirms the applicability and reliability of the proposed credibility estimator and its superiority in practical insurance applications.