The Principle Of Exponential Premium Of The Reliability Model

Reliability model is the model that adjusts its rate according to the claim experience of individual risk,and it is the most important achievement in non life actuarial actuarial science.It mainly studies how to make use of the prior information and individual claim experience to estimate,predict,and formulate the post insurance premiums.In rate determination,actuaries often need to refer to the insured's loss data over the past period to predict their future risk costs.However,because the loss data is from the insurance accident happened during the experience period,the data itself contains a lot of random fluctuations.It is not accurate to estimate future risks only by adopting these historical data.Reliability theory is one of the tools of this kind: using the reliability factor to ensure that the adjusted insurance premium is close to the real risk level.Premium pricing is the process that actuaries make a reasonable price for insurance products.When we make premium pricing,we must carry out scientific analysis and evaluation of future risks,so that insurance companies can claim on the one hand and earn profits on the other hand.If the premium is too high,the number of the insured will be reduced,and the insurance policy will be lost.If the premium is too low,the premium will not be enough to claim,which will bring losses to the company.Therefore,premium pricing is one of the most important issues of the insurance company.At present,the premium pricing theory of CITIC is the most effective method,it is a kind of experience that claim credibility models.The insured or portfolio based on past experience to determine or adjust future premiums.These years,this method has been widely used in non life insurance,liability insurance and life insurance.But the above theory also has its limitations.On the one hand,in the classical belief theory,the premium is obtained under the net premium,but therefore,it does not have a positive safety load,so it can not be applied directly in the actual insurance.And in fact,has proved that if the insurance company only charge the net premium will eventually lead to bankruptcy,the insurance company in order to solve this problem,the square loss function of classical reliability theory in the modified for other loss functions,so as to get some of the credibility premium premium principle.However,there will be a lot of restrictions in the actual use of insurance.on the other hand,in addition,the claim amount and the connection between the distance is different also,year's claim should be given greater weight.But both the classical reliability theory and later with dependent structure reliability insurance cost,they concluded that the reliability of the premium for different years claim,given the same weight.In actual use,however,claim and cheek by jowl with similar year,contact year far is relatively small.Claims for year closer to us,therefore,should be given greater weight,but the claims for the year far give less weight,this is more reasonable.In this paper,on the basis of the classical reliability theory,under the principle of index premium introduced a special kind of dependency structure of recursive reliability model.Got a future claim reliability insurance cost estimates.And give the corresponding reliability recursive form,thus promoting the classic theory of reliability.