Bayes Premium Under Maximum Likelihood Estimate

Based on historical records,Bayes Premium is the optimal choice under quadratic loss function.However,it cannot work because in general the distribution of risk parameters is unavailable.This paper presents a new kind of premium estimate,called New-Bayes premium,which is based on Credibility premium and the relationship between Bayes estimate and Maximum likelihood estimate.It works by limiting Bayes estimate to the linear combination of Maximum likelihood estimate.In the most popular EDF(Exponential Dispersion Family)distribution family,this new estimate has the same expression with Bayes estimate and Credibility estimate.While in multiple contracts,since it uses sample information to estimate the prior information,the detail format of prior distribution is not necessary.The simulation results show that this new estimate can reach smaller mean square error over Buhlmann's empirical credibility estimate.For the problem that Maximum likelihood estimate of parameters is unavailable for some distributions,this paper proposes an estimate asymptotically equivalent to the Maximum likelihood estimate,which is relatively easier to get in practice.