Analysis Of Credibility Model Based On Second-order Integer-Valued Autoregressive Process

Actuarial science is a discipline based on practical activities to solve quantitative problems in the fields of insurance,economy,finance and investment.It is based on relevant theories of mathematics and statistics.One of the core tasks of actuaries is the pricing of insurance products,which is of great significance to the business development and risk management of insurance operators.In the non-life actuarial process,the rate setting process usually consists of two steps: classification rate and experience rate.In the classification rate determination,we usually assume that individual risks belonging to the same risk category have the same potential loss,that is,each risk category is homogeneous,so they are charged the same premium.The experience rate is the cost of each hazardous unit calculated by the insurer on the basis of the average loss rate of the insured in previous years.The reliability theory is the main method to determine the empirical premium rate,which is to study how to estimate,forecast and determine the posterior premium rate by using the prior information and individual claim experience reasonably.Auto insurance,also known as motor vehicle insurance,accounts for more than 60 percentage of the total property insurance premium in China.The actuarial model of auto insurance pricing is an important research content in the field of non-life insurance actuarial.In the traditional auto insurance pricing,we usually use the classical Poisson gamma model and the reliability model based on the first-order integer autoregressive process to predict the reliability premium of auto insurance.However,for Poisson gamma model,the timeliness of historical claim data is not considered.For the reliability model of first-order integer autoregressive process,there are theoretical defects and inaccurate prediction results when predicting historical claim data with more years.To sum up,based on the first-order reliability model,this paper establishes a more practical second-order integer autoregressive process reliability model.Through numerical simulation,the theoretical superiority of the model is determined.Then,the Bayesian Reliability premium is estimated and inferred from the vehicle insurance data from 2006 to 2011 provided by lgpif to verify the accuracy of the model in practical application.