Credibility Model Analysis Based On NBINAR(1) Process

As an important financial means to avoid risks,insurance plays a vital role in the development of national economy.With people’s recognition and acceptance of insurance ideas and the popularity of various insurance businesses,actuarial science has gradually entered the public’s vision.Actuaries have developed a series of premium pricing criteria through mathematical and statistical modeling and quantitative analysis of different risks.For actuaries and insurance practitioners,how to optimize the rate determination method to get more reasonable and effective premium pricing criteria is one of the most urgent problems to be solved in modern insurance industry.In the field of non-life insurance actuarial calculation,the determination of a classification rate and a experience rate is one of the most critical links in the premium pricing process,and is also a hot topic in the study of scholars.A priori rate,also known as classified rate,classifies insured vehicles through the use nature of the vehicle or the owner’s age,gender,occupation and other risk characteristic information,considers that the insured under the same category has the same rate determination standard,and then uses the generalized linear model for rate determination.The disadvantage of this method of rate determination is that the risk characteristics of each insured person are uncertain in the actual situation,and actuaries cannot guarantee that their assigned categories apply to every policyholder.The posterior rate just makes up for the above deficiencies.The posterior rate refers to the historical claim data unique to each policyholder and adjusts the prior rate to get the policy holder’s own rate,which is also known as the empirical rate.The reliability model is one of the most important methods to determine the posterior rate.In this paper,a new class of integer time series credibility model,called the credibility model of first-order integer-valued autoregressive(NBINAR(1))process based on negative binomial thinning operator,is studied,and the Bayesian reliability premium under this model is calculated.Then,numerical simulation is conducted to compare the results of Poisson-Gamma model,INAR(1)model based on binomial sparse operator and the model proposed in this paper under the conditions of given different historical claim data.It is found that the model proposed in this paper can obtain more realistic results in the simulation.Finally,the NBINAR(1)model is used to analyze the 2006-2011 old car collision insurance data set provided by the local government of Wisconsin,USA.In order to compare the prediction performance of the Poisson-Gamma model,the INAR(1)model and the NBINAR(1)model,the previous 5 year data were used as training samples and the inar(2011)year data were used as test samples.The results show that the NBINAR(1)model has the least error.The rationality and superiority of NBINAR(1)model are proved.