Credibility Theory Under Dependent Risks And Asymmetric Loss Function

In the insurance company,one of the most concern is how to make the premium scientifically and reasonably.In the formulation of premium,not only to consider a priori information,but also to consider individual claims experience,reliability theory provides a good tool for this.The origin of modern reliability theory in Bühlmann.Bühlmann estimated the linear function defined in the claims data,the claim is not required,the Bühlmann model,laid the foundation of modern reliability theory.In the classical theory of reliability,we always assume the risk are independent of each other,but in the insurance practice,this independence assumption is often not valid,so it is necessary to consider the dependence of the risk in the original model of development.Classical reliability theory,commonly used square loss function to measure the risk,compared to the symmetric loss function,the asymmetric loss function can better measure the risk,which makes the premium collection more reasonable.In this paper,asymmetric loss function Stein loss function as an example,consider the case of Dependent Risks under Stein loss function,the original model is extended by Bühlmann model and Bühlmann-Straub model with time variation effect.