Research On Several Credibility Estimator Problems Of Risk Premium With Dependent Structure

Credibility theory is a set of experience ratemaking approaches which has been widely used in insurance companies' premium pricing.In the classical credibility model,under the assumption that the risk is independent of each other and the historical claims are conditionally independent and identically distributed given risk parameters,by solving the expected square loss minimum problem,we can derive the credibility estimation formula of the future claim.In fact,in practice,the risks are not always independent.There may exist a certain depen-dence structure over risks.Meanwhile,the claims are not always conditionally independent and identically distributed.In recent years,credibility models with dependence structure have drawn great attention.However,there is few research effort that accommodate simultaneously the conditional dependence across the time horizons and the dependence over risks.To meet actual needs,this thesis studies several credibility estimators of risk premiums with dependence structure.The main contents are as follows:Chapter 2 studies the credibility estimators with equal correlation structure over risks and time under balanced loss function.Firstly,we present the related concepts and conclusions of orthogonal projection.And then,by using the orthogonal projection approach,we derive the inhomogeneous and homogeneous credibility estimators of the future claim in the Buhlmann model with equal correlation structure over risks and time under balanced loss function.Further-more,the corresponding results are extended to the Buhlmann-Straub model and the estimation of structural parameters is discussed.Finally,numerical simulation is provided.Chapter 3 discusses the multidimensional credibility estimators with time effect and com-mon effect.First,we introduce the research background of multidimensional credibility model.Then,by applying orthogonal projection approach,we obtain the multidimensional credibility estimators of the future claims in the Buhlmann model with time effect and one level common effect under quare loss function and also discuss the estimation of structural parameters.In the third section of this chapter,we investigate the multidimensional credibility estimators with time effect and two levels common effects under the balanced loss function.Finally,we present a numerical example to show the difference between our results and the classical multidimen-sional credibility estimator.Chapter 4 studies the credibility model with dependence over risks and over errors un-der the exponential premium principle,in which we mainly extend the credibility model with independence over risk and time under the exponential premium principle to the model with dependence structure over risks and over errors.Firstly,we present the definition of risk premi-um under the exponential premium principle.Then,by the orthogonal projection approach,we derive the credibility estimators of risk premium in the Buhlmann and Buhlmann-Straub with dependence over risks and errors under the exponential premium principle.Chapter 5 still discusses the credibility estimators of risk premium under the exponential premium principle.Different from the chapter 4,this chapter considers the dependence over portfolio risks,over individual risks as well as across time horizon,and studies the credibility model with time effect and two level common effect under the balance loss function.First,we give the assumptions of the model,and then obtain the inhomogeneous and homogeneous credibility estimators of the individual premium in the Buhlmann and Buhlmann-Straub models with this dependence structure.Chapter 6 studies the regression credibility model with two level common effects.In this chapter,we first introduce the origin of the regression credibility model.Then,under the cor-responding model assumptions,we obtain the credibility estimators of the future claim and the random regression coefficient and discuss the special case of these estimators.