Bayesian Statistical Analysis Of Quantile Premiums

Quantile premium principle is an important principle of premium,It requires that the probability which the premium is less than risk loss random variable is no more than the given small probability alpha.The premium principle on intuitive is easy to understand,And it can meet some important properties,Therefore,It has important applications in insurance actuarial,In practical application,Because the quantile premium depends on the specific distribution of risk,Quantile premium is unknown,we need the existing information to estimate it.In the process of estimating quantile premium,There are two types of information which is available for us.One kind information is a priori information which we can get from the existing material and the empirical data of the risk,Another kind information is sample information which we can get from observing the risk.Our goal is to synthesize the priori information and the sample information to estimate the quantile premium,and we will do the corresponding study of statistical inference.The bayesian model of the quantile premium principle is established in a variety of risk model in this article,Quantile premium's estimates under all kinds of risk model are got,And the properties of these estimates are discussed,Consequently,The result will be applied in the insurance practice.The basic methods of bayesian analysis?Bayesian statistical inference principle and the selection rules of the prior distribution are introduced,etc.And then,The common Premium Principles that are used in insurance actuarial are introduced,too.Particularly,This paper focuses on the definition and property of the quantile premium principle in the second chapter.we establish Pareto risk model,And put forward the corresponding loss function,we also obtain bayesian estimation and bayesian premium of the quantile premium,And study the statistical properties of these estimates,In the end,The mean square error(mse)of these estimates and maximum likelihood estimation of the quantile premium are compared in the third chapter.Index risk model of the quantile premium is established,The selection method of the prior distribution of the risk parameter is given.Then bayesian estimation of the quantile premium is obtained.Finally,according to the empirical bayes method,The moment estimators of the structural parameters and their property are studied,The progressive optimality of the empirical bayesian estimation is proved in the fourth chapter.The full text is summarized in the fifth chapter.