Research On The Prediction Of Premiums In Linear Model And Generalized Linear Model

In actuarial science,the insured transfers the possible risk to the insurance company by paying a fixed amount,which is called premium.If the premium is too high,it is easy to lose the insurance policy;if the premium is too low,it will lead to the loss of the company.Therefore,premium pricing and forecasting has always been the most concerned issue of insurance companies.In the pricing process,not only the risk factors(prior distribution information)but also the historical claim experience(sample information)should be considered.The most commonly used method is credibility theory.However,in real life,there are a variety of risk factors that will affect the claims of insurance policies,the prior distribution is difficult to determine,often only know the sample information.Based on a series of historical claim data of insurance policies,this paper puts forward some methods for forecasting future claims.Firstly,with the idea that the prediction of future claims is limited to the sample linear function in the credibility theory,the problem of claim credibility prediction under the linear model is discussed by using the method of minimizing the mean square error.The estimated premium can be written in the form of credibility premium,and its statistical properties are verified by numerical simulation.Then,the method is extended to the more widely used generalized linear model,and similar conclusions can be obtained in the linear model.Secondly,the prediction problem of aggregation risk model with more complex structure is discussed.At present,most of the research on the total claim amount is based on the net premium principle,which is difficult to apply to the general premium principle,and many premium principles can be obtained through the moment generating function of risk.To solve this problem,based on the claim data,this paper establishes a generalized linear model of moment generating function related premium principle,and obtains the prediction of total claim under moment generating function related premium principle by predicting the moment generating function of claim amount and claim times.Finally,the whole paper is summarized and the directions of further improvement are suggested.