Study Of Regression Credibility Under Balanced Loss Function

Credibility theory is a rating premium technique that predict the premium in the next year,which is based on historical claims data and a prior information.Actuaries analyze the historical claims data of insurance products,and make a pre-mium according to the distribution characteristics of risk random variables.We define a possible claim caused by a policy as a risk X,and describe the risk with the risk parameter θ.The credibility premium is estimated by the linear function of historical claims in the next year.Buhlmann established the non distribution credibility and obtained the expression of credibility premium under the square loss function.However,considering the influence of inflation,Hachemeister proposed a regression model to describe the time effect and established the regression credibility model.Then,the regression credibility model embedded into various forms of credi-bility model under the square loss function.However,in practical application,if we use other loss functions to study the regression credibility models,we can further generalize the regression credibility model.The main work of this paper is to study the regression credibility model under the balanced loss function,using the projection formula in the credibility theory to explore the regression credibility model,on this basis,the regression credibility estimation method is proposed.First,the regression credibility estimation of net premium is obtained by transforming the balanced loss function into the square loss function,furthermore,the projection formula of balanced loss function based on this method is introduced,and then the Bayesian linear regression credibility model under the balance loss function and the estimation of the common effect regression credibility model are derived.Finally,the unbiased estimation of the parameters in the common effect regression credibility model is given.The regression credibility estimation expression obtained in this paper still has the form of credibility.In this model,a certain target estimation of the estimation variable is considered,and a certain weight is given to the target estimation in the estimation form.In practice,when making the premium according to the regression credibility model under the balanced loss function,the corresponding premium is selected by adjusting the weight of the balanced loss function.This model is more flexible than the credibility model under the square loss function.The regression credibility model under the square loss function is a special case of this model.The common effect regression credibility model under balanced loss function in this paper is an extension of common effect credibility model under the balanced loss function.