查看原文: in ins rance practice, one of the cr cial tasks of act aries is to determine adeq ate premi ms to be charged for risks and there have been a variety of in-s rance pricing methodologies to serve this p rpose. credibility ratemaking is a techniq e for predicting f t re claims of a risk class, given past claims of that and related risk classes. mowbray (1914) provided an early introd ction to practical aspects of this techniq e. b hlmann (1967) derived a credibil-ity form la which has the form of weighted s m of the individ al mean and the overall mean in a distrib tion-free way by sing a least-sq ares criterion and thereby placed credibility ratemaking on a firm modeling fo ndation. s bseq ent some important credibility model appear like b hlmann-stra b model, hachemeister model, hierarchial credibility model. in fact, it has been recognized that there exist many important ins rance scenarios where these classical ass mptions are certainly violated and the dependence over risks are common. the b hlmann and biihlmann-stra b models with de-pendence str ct re were st died in many cases. in classical decision theory, the loss f nction s ally foc s on precision of estimation. however, goodness of fit is also a very important criterion. th s there is a need to provide a kind of comprehensive estimation. a pioneer work zellner (1994) introd ced the notion of a balanced loss f nction (blf) in the context of a general linear model to reflect both goodness of fit and precision of estimation. credibility ratemaking nder balanced loss f nction has st died in recently year. the credibility models for the weighted premi m principle s ch as esscher pre-mi m principle, modified premi m principle also have been disc ssed beca se they can be red ced negative safe loading ca sed by net premi m principle. this thesis is concerned with two aspects of the credibility estimators of risk premi ms which is different from classic credibility model in risk str ct re and loss f nctions, described in detail as follows.the first part of thesis incl des chapters2,in which we extend the cred-ibility models with dependence str ct re over risks. the credibility model with dependence over risk and time. firstly we give the relationship be-tween orthogonal projection and credibility estimator and the form lae of credibility estimator by applying orthogonal projection techniq e. by the orthogonal projection techniq e, we derive the inhomogeneo s and homoge-neo s credibility estimator of risk premi m in b hlmann with dependence over risk and time. the inhomogeneo s credibility estimator with common effect which means the special correlation between risks is given. at last we obtained the inhomogeneo s and homogeneo s credibility estimator of b hlmann-stra with dependence over risk and  the second part, we foc sed the credibility estimator nder the bal-anced loss f nction and weighted q adratic loss instead of being disc ssed nder q adratic loss in classical credibility model. in chapters3, firstly the relation between the credibility premi m nder balanced loss f nction and q adratic loss f nction is given. the general credibility premi m with depen-dence over risk and time nder the balanced loss f nction is established. the inhomogeneo s and homogeneo s credibility premi m with common effect is derived while some str ct re parameters in credibility form la is given. at last the credibility premi m of exponential premi m principle nder balanced loss f nction is  chapters4, firstly the linear regression credibility premi m with corre-lation risk nder balanced loss f nction is derived. partic larly the credibility premi m was expressed when the target estimator in balanced loss f nction is specialized, meanwhile the credibility linear regression model with eq al cor-relation risk and common effect nder balanced loss f nction was disc  chapters5, q adratic error loss in classical credibility model is re- placed by weighted balanced q adratic error loss beca se the missing of safety loading is ca sed by the loss f nction. firstly a new expectation with respect to a new probability meas res which is determined by weighted f nction and ass med probability meas res is given. the credibility premi m with simple b hlmann model nder some weighted balanced q adratic error loss are ded ced firstly. then the consistency of credibility premi m nder weighted balanced q adratic loss f nction is disc ssed. at last, based on the disc ssing of credibility premi m weighted balanced q adratic error loss, we foc sed on the premi m nder general weighted balanced loss f nction lpρ,ω,δ0(θ,δ)=ωρ(δ0,δ)+(1-ω)ρ(θ,δ). the credibility premi m nder bal-anced entropy loss f nction and balanced linex loss f nction are ded ced by taylor expansion.