Estimation Of Parameters And Prediction Of Frequency Risk Models

Real-world experience rating schemes are the main gists in premium pricing in property-liability insurance.Accordingly,the claims in history have compact relationship with experience rating schemes.Random effect is induced into numbers of claims models in frequency risk models which are studied in this paper.The parameters of mixtures of Poisson distributions are described with random effect and regressive parts.Discussion is developed from this.Next is the main work of this paper.1. Induce the random effect into frequency risk models;in the same time bring forward assume of stationarity.2. Estimate the parameters basing on Maximum Likelihood Estimation.The estimation is from the condition without random effect to the condition with .The method is developed gradually.3. Get the estimation of random effect with the bunus-malus coefficients and the second-order moments of random effect.4. Beginning with AR(p)-ARCH(q) models,as well as KIC method , confirm the order p,and predict the random effects.5. Do the numerical simulationsThe following is the structure of this paperThe first chapter is exordium.This part introduces the basic knowledge,i ncluding Poisson distribution,white noise,AR(p) and ARCH models and so on.The second chapter is the establish of the models and estimation of the parameters. At first,induce the concept of random effect,then raise the hypothesis,establish the models and estimate the parameters , after that use credibility theory to get the linear credibility predictor, and estimate random effect.Finally,get the prediction and write out the method of confirming order.The third chapter is the simulation of the second part,which is composed of estimation of parameters,confirming the order of AR(p) and confirming the order of ARCH(q). The last part is conclusion.