Credibility Premium Under The Weighted Loss Function

Credibility theory is one of the important branches of both risk theory and non-lifeinsurance, it is a kind of method to calculate the future premium based on the historicalexperience of a single policyholder and the entire group of policyholder as well as the sim-ilar policy, this method is widely used in every field of insurance practice. The credibilitypremium, which computed from credibility theory, is generally the weighted average ofindividual claim data and transcendental premium(or the similar insurance data at thesame time ) , and the weighted factor is credibility factor.In the credibility theory, it is an important thing to choose the loss function. AfterBu¨hlmann adopted the Square Loss Function to calculate the future premium in his clas-sical credibility model , many scholars make some research on the loss function. For thispaper , we use the method of the Relative Mean Square Error Loss Function of the Order pto structure the Relative Balance Loss Function of the Order p1 and the Relative BalanceLoss Function of the Order p2, and then we calculate their credibility premium and thecredibility factor. The result turns out that these two loss functions are the generalizationof the Balance Loss Function1 and the Balance Loss Function2 respectively. After that, wetake the idea in Pan.M's paper to amend the credibility premium under the GeneralizedWeighted Esscher Loss Function, and get a better premium.