A Class Credibility Models With Positive Safe Loading

Credibility theory plays an important role in the non-life insurance actuarial theoryand practice, it’s a kind of quantitative approach to generate the future insurance pre-mium based on the historical experience of a single policyholder and the entire group ofpolicyholders. In general, the most credibility premium is the weighted sum of average ofthe individual premium and collective premium, the weighted factor is called credibilityfactor. Thus the formula can easily be implemented in practice due to its simple form inmathematics. This approach is widely used in the various areas of insurance practice.Bǔhlmann adopted square loss function in his classical credibility model and obtainedthe formula of the credibility premium by least squares method. After Bǔhlmann, someresearch on how to choose the loss function was found in many papers, In fact, in theclassical credibility premium model, the credibility premium is derived on the basis of purepremium, but in the insurance practice, insurance companies charge the premium can notbe pure premium, otherwise insurance companies will face bankruptcy, so the premiummust have a positive safety loading. In this case, the insurance practice need to considerthe appropriate premium principle to determine the premium, In this paper, frstly, we getthe weighted balanced credibility model on the basis of the exponential premium princi-ple. And then, we derive the Bǔhlmann and Bǔhlmann-Straub credibility formula underan equal correlation structure over errors and risks At last, considering the the historicalclaims as random variables are independent with the diferent distributions, further obtainthe more general single contract and multitude contracts credibility premium under theexponential premium principle.