The Credibility Models Under Dependent Risks

In the insurance companies, premium pricing (forecast) is one of the important tasks foractuary. During the process of pricing the premium, the actuary should analyze and model themulti-policy risks scientifcally for the purpose to develop an appropriate premiums. Credibilitytheory is the main method of premium pricing models. It is usually assumed that risks are in-dependent among each other in most of the premium pricing models due to the consideration formodel simplifcation. However, risks are often presented to be dependent on each other because ofthe complexity of risks. For example, many cases have shown that the life span of one couple isdependent on each other, the neighboring houses may face a common risk of fre, residents in thesame city face the same earthquake risk and so on.The thesis mainly discussed the credibility models of for single contract with dependenceinduced by time changeable efects and the dependence between two or more risks. Under thedependent structure of risks, we obtained the predictors for future premium. Finally, the premiumprediction method are applied to the GDP forecast, and get desired conclusion.In the second chapter, the credibility premiums with time changeable efects are derived bymeans of credibility theory methods. The results showed that credibility estimator of the credibilitymodels with time changeable efects can still be expressed as weighted sums of claim data andcollective premium, and the credibility factor depended on the time changeable efects. Thus theclassical credibility theory is generalized. Finally, the method is applied to predict China’s GDPforecast. If we consider the diferent provinces as multiple contracts, and the GDP data in diferentyears are taken as individual contracts for each claim amount (rate), then our provincial GDP datais exactly consistent with credibility model’s data structure. In the credibility models with timechangeable efects, we aimed to get the credibility prediction about the GDP data of2013andseveral years later. The results showed that the prediction method has high accuracy.In the third chapter, we discussed the credibility models under the condition of dependentrisks. Pay attention to the classical Bu¨hlmann credibility models, each risk of contract is assumedto be mutually independent. This chapter introduced a dependence among risks and developeda credibility model under some special risk dependence. Through the method of orthogonal pro-jection, it is given the corresponding model of credibility prediction for future claims. The results showed that the credibility estimators are remain the weighted sums of individual and collectivepremium.