Further Study On Credibility Theory Under Balanced Loss Function

The balanced loss function refects both precision of estimation and goodness of ft,it has been the subject of many theoretical and applied studies. So this paper makesfurther research on credibility theory under balanced loss function.First, in the classical credibility theory, the credibility premium are derived on thebasis of pure premium. However, the exponential premium principle satisfes all pros-perities of premium principle, so the insurance company often decides the premium byusing it, in literature [27], Wen et al. obtained the credibility estimators of exponentialpremium principle under squared-error loss function. This article established credibilityestimators of exponential premium principle under balanced loss function, it generalizedWen et al.’s conclusions.Second, in practical applications, with prices of commodities changing every year, theinfation’s infuence towards claim amounts should be considered. So our article studiedthe credibility premium with infation factor under balanced loss function, obtained thesingle contract model and multiple contracts model’s premium and simulated the resultswhich showed the desired conclusions.Third, in the classical credibility theory, the risks in a portfolio are assumed tobe independent, but in insurance practice, it isn’t independent among risks and it hasdependence structure among risks, in literature [28], Wen et al. obtained the credibilitypremium with time changeable efects under squared-error loss function. So we maderesearch on credibility models with this special dependence structure under balanced lossfunction, obtained Buühlmann and Buühlmann-Straub models’ premium, it generalized theclassical credibility models―Buühlmann and Buühlmann-Straub models.