Reasearch On The Non-life Insurance Outstanding Claim Reserve Based On Double Bayesian Model

The outstanding claim reserve is the largest debt for non-life insurance companies and plays an important role in the operation of insurance companies.However,many companies have gone bankrupt or incurred bad debts due to unreasonable reserve in recent years.Therefore,how to reasonably evaluate the outstanding claim reserve has become a key concern of insurance companies.At present,the deterministic methods and the random methods are the main methods to evaluate non-life insurance reserve,but they have the defect of not making full use of the known data and only using the single variable of the amount of compensation,thus reducing the prediction accuracy.The distribution of parameters in the model is not considered in the study of the number of claims and the average amount of claims to be assessed by the GLM.For a more accurately evaluate the outstanding claim reserve,this paper analyzed the necessity of studying the outstanding claim reserve based on the two variables of claim number and case average indemnity,and established the double Bayes model to estimate the claim number and case average indemnity respectively,taking into account the unobservable factors.The empirical results show that the prediction accuracy of the outstanding claim reserve is greater on the basis of unobservable factors and two-stage evaluation.Due to the absence of prior information,existing studies have set the prior distribution's(Gamma distribution)shape parameters of the progression year and occurrence year factors to zero and infinity,which makes it impossible to accurately evaluate the outstanding claim reserve.In this paper,the known information is used to try to use the least square method to estimate the parameters of the Gamma distribution in the prior distribution of the accident progression year,and the shape parameters in the prior distribution of the accident occurrence year are set as zero(that is,no information priors)and infinity(that is,strong information priors).The empirical results show that the model proposed in this paper can obtain more accurate prediction results on the basis of estimating the prior distribution parameters under the full consideration of the influence of the accident progression factor and occurrence factor on the outstanding claim reserve.This paper first briefly introduces the non-life insurance the outstanding claim reserve and the basic model used,then improves the prediction model of the number of claims and the case average amount of claims.The Bayesian model was introduced to depict the unobservable factors in non-life insurance practice,and the Bayesian ODP-Gamma model was constructed for the number of claims,and the Bayesian exponential-Gamma model was constructed for the case average amount,and the Bayesian ODP-exponential Gamma model was established to predict the non-life insurance outstanding claim reserve.In order to describe the prediction error of the model,this paper gives the theoretical derivation and estimation method of the mean square error of the model.Empirical analysis shows that unobservable factors,namely the value of prior parameters,can affect the predicted value of the outstanding claim reserve and its prediction effect.With the increase of information collection,using this model can improve the prediction effect and application scope of the outstanding claim reserve.This paper puts forward a new exploration and thought for the research of the outstanding claim reserve.