Linear Bayesian Prediction Of Discrete Random Variables And Its Application

In non-life insurance actuarial,insurance companies often care about the number of expenditures of a policy,and it reflects the risk of the policy.If the number of claims can be predicted from historical data,then the policy pricing will be more reasonable.The number of claims often depends on the risk characteristics of the policy,and the synthesis of these risk characteristics is generally characterized by a certain risk parameter θ.Due to the non-homogeneous policy,the risk parameter θ is considered to be a random variable,subject to a prior distribution.Therefore,the prediction of the number of claims falls into the Bayesian framework.Assuming that the policy has lost records of the number of claims in the past several years,this paper predicts future claims based on the sample record of the policy portfolio and the prior distribution of risk parameters.This paper studies the prediction of discrete random variables with non-negative integer values in non-life insurance actuarial calculations.In the second chapter,the Bayesian model of discrete random variables is established.According to the prior information of the number of observed claims and risk parameters,the prediction of future claims is proposed.According to whether the conditional distribution of the number of claims and the prior distribution of risk parameters are known,it is divided into three cases for discussion,and the differences of Bayesian predictions under different loss functions are compared.Due to the impact of deductibles and no claims preferential treatment system,a large number of low-loss policies have not made claims,which has magnified the number of policies with zero claims.In Chapter Three,the risk parameters of three loss functions under the zero-inflated Poisson model are studied Bayesian estimation,and using the theory of credibility to study the credibility estimation of risk parameters,and then compare the goodness of Bayesian estimation by numerical simulation.Chapter 4 studies the application of Bayesian prediction of discrete random variables in journal classification.A Bayesian model of periodical quality is established.The Bayesian estimation of periodical quality parameters is studied under the exponential family distribution,and the statistical properties of the estimation are discussed.The method of estimating hyperparameters is discussed,and the moment estimation and marginal maximum likelihood estimation of hyperparameters are given.The numerical statistical method is used to verify the statistical properties of the estimates,and then a correction formula for the journal quality impact factor is given for domestic mathematics journal citations for empirical analysis.In the end,the full text is summarized and the directions for further research are put forward.