Credibility Premium Under The Generalized Weighted Esscher Loss Function

Credibility theory is a kind of quantitative approach to calculate the future premiumbased on the historical experience of a single policyholder and the entire group of pol-icyholders. This method is widely used in every field of insurance practice. Generallyspeaking, credibility premium is composed of the weighted average of individual premiumand collective premium, weighted factor is credibility factor. Bu¨hlmann adopted squareloss function in his classical credibility model and obtained the expression of credibilitypremium with least squares method. Esscher loss function, also called exponential lossfunction has parameterαwhich is named adjustment coe?cient in ruin theory, it hasprofound significance in practice.In this paper, we firstly generalize Bu¨hlmann credibility model based on the general-ized weighted loss function, and then deduce the credibility formula under the Esscher lossfunction. At last, further obtain the more general credibility premium under generalizedweighted Esscher loss function.