Some Extensions Of The Credibility Estimate In Risk Pricing

Credibility theory is a kind of quantitative approach.Insurer can use the method tocalculate the experience premium based on a single or a group of risks,that is accordingto the underwriting experience to adjust future premiums.Generally,credibility premiumis composed of the weighted average of individual premium and collective premium. Inthe classic single contract Bu¨hlmann credibility theory,the insured's historical claims areindependence and identically distributions under the hypothesis of giving the risk.In theBu¨hlmann-Straub credibility models,while giving the risk, variance is proportional torisk.In recent years, by the methods of adding dimensions, transforming loss functions,and considering the risk of non independence,people get a lot of general credibility models.In this paper,we frstly obtained the independence and unbiased of a more generalform of the mean value under the conditions of special exponential distribution fam-ily.Then,we get the improved credibility estimate under the generalized weighted Esscherloss function. Finally,we introduce a generalized linear mixed efect credibility modelswith random common efect structure and obtained the credibility predictors of futureclaims and the estimators of risk parameters.