Statistical Inferences Of The Risk Premium Under The Two-parameter Exponential Premium Prnciple

The exponential premium principle is an important principle in non-life actuarial science,and it is also one of the most used premium principles in practice-This paper proposes an improved ex-ponential premium principle-the double-parameter exponential premium principle.This premium principle can not only incdude the principle of exponential premium,but also is a generalization of the Esscher principle and the exponential premium principle.It satisfies many theory properties including non-negative safety negative loading,transfer invariance,no unjustified risk loading,ad-ditivity for independent risks and continuity.In this paper,the estimation and prediction of risk premium under the double-parameter exponential premium principle are considered.In Chapter 2,the backgrounds are introduced and the principle of two-parameter exponential premium are pro-posd.In Chapter 3,the nonparametric and maximum likelihood estimations of the two-parameter exponential premium are given,and the large sample property of the estimation is proved.By us-ing the numerical simulation method we compare the mean square error and the convergence speed of those estimators;In the fourth chapter,the Bayesian model of the two-parameter exponential premium principle are given.The Bayesian estimation and Bayesian predictor are derived,and the consistency of those estimators are checked.In the Poisson-Gamma model,the expression of the formulae of the Bayesian estimate are given,and the strong consistency and asymptotic normality are proved.In chapter 5,the two types of credibility estimates including plug-in type and loss function type for risk premiums are given under Bayesian models.The large-sample property of credibility estimation are proved.We also compare the mean square error between the credibility estimators and Bayesian estimators in this chapter.The convergence rate of the estimation are also checked.