| Credibility theory is devoted to calculate the credibility estimate of premium of corresponding risks based on the the historical experience of a single policyholder and the entire group of policyholders,In general,the most credibility premium is the weighted sum of average of the individual premium and collective premium,the weighted factor is called credibility factor.This method has been widely applied to the various areas of insurance practice.on the one hand,we establish recursive credibility model under maximum en-tropy method,which aims to minimum the mean squared errorand and maximum the entropy.we also deduce the expression for credibility premium and credibility factor.At the same time,we show special cases of credibility model.one have larger weight in recent years,another have smaller weight in recent years,which generalizes the classical credibility theory.on the other hand,the credibility premium is on the basis of pure premium,which can not be used in the insurance practice,therwise insurance companies will face bankruptcy.One of the method to solve the problem is to change the loss function,in the paper,we aims to establish recursive credibility model under Ess-cher Loss function and deduce recursive credibility under generalized Esscher Loss function.finally,we will futher study dependence credibility model including inhomoge-neous and homogeneous credibility estimator. |
