| A remarkable characteristic of insurance industry is indebted manage-ment.Insurance companies manage and operate insurance funds formed by premiums paid by customers to achieve the purpose of spreading risks and obtaining profits.However,insurance companies have great uncertainty about the liabilities of customers.For an insurance contract without expiration,it is impossible to determine whether there will be an accident.Even knowing what has happened doesn’t,always lead to a quick determination of the final claim.Therefore,the insurance company must regularly evaluate these out-standing liability and make a reasonable capital reserve for the outstanding liability of the effective policies it underwrites,which is the claim reserve.The largest liability,on the balance sheet of a non-life insurance company,is always the claim reserve,The accuracy of claim reserve is directly related to the ade-quacy of the indemnity capacity and the considerable performance of non-life insurance companies.In this paper,we introduce the mathematical framework of claim reserve from the perspective of measure theory,and prove the martingale property of claim reserve theoretically,which is the theoretical basis for the prediction and estimation of claim reserve.Auto insurance data were selected as evalu-ation objects,and claims reserve was evaluated by chain ladder method,B-F method,randomness method based on log normal distribution model and Kalman filtering method.Chain ladder method and B-F method are both eval-uation methods based on the assumption of no distribution.As a further study,considering the randomness method based on the distribution model,the log normal distribution model is one of the distribution models for the claim re-serve assessment.However,the three methods still remain static analysis.Once significant fliuctuations or outliers occur in historical data,the procesing of such fluctuations or outliers will affect the accuracy of t.he evaluation results.As a dynamic method,Kalmnan filter can solve the problem of historical data fluc-tuation and outliers by iteratively updating the estimated values of parameters and processing autoregressive data.Empirical results show that,the longer the progress is,the more significant the advant,ages and effects of Kalman filtering method become. |
