The Application Of Bayesian Method In Actuarial Model

With continuous development of the theory of probability and statistics, the Bayesianmethod shows its unique advantages gradually, and forms a very influential school ofthought, and its influence continues to expand, even every field of human studies exists acertain level of bayesian analysis.The research and application of the Bayesian method inactuarial mainly divided into the following three aspects: experience rate estimation, lossreserves and compound loss models, updating data and life table.In this paper,we summarized the origin of the development of the Bayesian methodand the present status of research both at home and abroad,expounded the reasoningthinking of the Bayesian method and the steps of parameter estimation,detailed thebayesian reliability estimation,derived several important conclusions,clarified therelationship between the bayes premium and some important estimator,and focused on themethod of determination and selection of prior distribution and several conclusions inconjugate prior distribution.No matter in which aspect, the study of model is top priority.This article mainlyintroduced the linear reliability model,the graduation model,the MCMC model and thetime series regression model.The Buhlmann model,the Buhlmann-Straub model and theirempirical bayesian estimation were deduced in the linear reliability model,and theirapplied range and computational process were illustrated.The Kimeldorf-Jones methodand the Dirichlet method were introduced in the graduation model,and the general form ofestimator of graduation were obtained.The theory of MCMC model and the steps of itsapplication were introduced. The AR(p) model and the MA(q) model were introduced inthe time series regression model, and the expressions of parameter estimation andpredictive distribution were deduced.Finally,the application of the Bayesian method toclaim frequency and premium were given in four numerical examples.