The Research Of Credibility Premium With Double Common Effects

In all sorts of insurance practice, one of the most concern of the insurance company ishow to scientifc and reasonable premium pricing. So far, researchers have proposed manymethods to determine premium, the credibility theory is widely used as an importanttechnology, the credibility theory is a technique for predicting future claim of a riskclass give past claims of that and related risk classes. At the beginning of20th century,credibility theory has emerged, Bü hlmann derived a credibility formula which has theform of weighted sum of the individual mean and the overall mean in a distribution-freeway by using a least-squares criterion and thereby placed credibility ratemaking on afrm modeling foundation,it will combine the development of the theory of credibility andstatistical techniques.Classical theory of credibility, are usually based on the independence structure be-tween individual and on the independence of the time, but in the modern life, this inde-pendence assumption is often not set up, in many cases there are dependencies betweenrisk group, risk also has time efect between diferent years, therefore, to introduce theconcept of double common efects. In addition, in order to avoid bankruptcy, the in-surance company needs to consider the positive safety load of the premium, thus, theintroduction of index premium principle, under the condition of the given credibility pre-mium. Estimates of the premium, the classical decision theory focuses on the estimationprecision, without considering its degree of ftting, so Zellner frst introduces balancedloss function, at the same time refected the general linear model precision and ftting.In the credibility theory, the balanced loss function has also been widely used.In this paper, we frstly generalize B ü hlmann credibility model based on the credibil-ity premiums with double common efects, and then deduce the credibility formula underthe exponential premium principle. At last, further obtain the more general credibilitypremium under balanced loss functions.