The Posterior Ratemaking of Premium in Binary Bayesian Collective Risk Model

In the Collective risk model, the claim amount is divided into large claims and small claims. Under the variance-related premium principle, the Bayesian estimation of the risk premium in the binary Bayesian collective risk model is derived. The conclusion shows that both the conditional expectation and conditional variance parts of risk premium can be expressed as a weighted form of sample function and aggregate premium, where the weight satisfies the property of ``credibility factor''. Furthermore, the strong consistency and asymptotic normality of Bayesian estimation is proved. Finally, the method of numerical simulation is used to verify the large sample properties of Bayesian estimation.