Estimation for Claims Reserving Based on Bayesian Over-dispersed Poisson Model
|Keywords||Claims reserving Over-dispersed Poisson model MCMC|
As an important debt item of Non-insurance company, Outstanding claims reserve will directly affect the company’s operating condition, the current domestic and foreign insurance companies are exploring more precise model in outstanding claims reserves. how to draw reserve for outstanding losses have been a continuously explore and strive task of companies. For estimates outstanding claims reserve, the insurance industry at home and abroad mainly used deterministic methods, such as the chain ladder method, the average loss method, the loss ratio method and BF method, but these methods are often too simple, intuitive and idealistic assumptions. Stochastic model can provide outstanding claims reserve point estimate, interval estimates and the corresponding statistical test, in recent years, stochastic models are more and more applied to non-life insurance claim reserves.In this paper, We based on the deterministic model, consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. Considering the progress in factor and factor’s influence on the loss reserves estimation, We choose different types of prior distributions for the parameters and then study the different Bayesian predictors. Because B-F method use the full priori information, and CL method use no priori information, this article is trying to have different intensity of a priori information into the over-dispersed Poisson model, makes the model not only confined to the chain ladder method and random model of B-F method, but can provide a series of Bayesian over-dispersed Poisson (ODP) model, the chain ladder method and B-F method just as special cases of these models.In the empirical part of the paper, we based on the car insurance data, using the WinBUGS software and the MCMC method and Gibbs sampling to simulation.First obtain the the estimates of the outstanding claims and estimation error.And then compared the Bayesian over-dispersed Poisson (ODP) model,the chain ladder method, B-F, generalized linear model.The model of this paper not can only obtain outstanding claims, but also can get the complete posterior distribution density function estimation, the estimation error, distribution, etc.In addition, it give full consideration to the inner relationship of the development factor and internal factor,so the prediction results more close to the truth.