Payments Per Claim Method On Kernel Smoothing And Fuzzy Linear Regression

The outstanding claims reserve is an important liability of non-life insurance companies,and is closely related to the insurance company's ability to pay and the interests of the insured.Therefore,research evaluation reserves help insurance companies to reserve more accurate reserves with important application value.The payments per claim method is widely used because of its simplicity of operation and avoiding waste of information.However,it can only achieve point estimates for pending reserves,but cannot measure its uncertainty.And volatility,in view of this,this paper introduces the kernel smoothing function in the traditional payments per claim method for the randomness method.In practice,the liability reserve assessment is based on past experience to predict future claims,but historical data will be limited in terms of data quality,and estimates of reserves will be subject to inflation and other variables influences.There are uncertainties in these factors,and the values of historical data are also ambiguous,so the assessment of outstanding claims reserves is also ambiguous.The traditional case compensation method can't solve this problem.Therefore,this paper introduces the fuzzy linear regression method into the payments per claim method,which improves the estimation accuracy and helps the company to provide more accurate reserves.This paper introduces the improvement of the average compensation method.Combining the nuclear smoothing with the traditional payments per claim method,the model of the average compensation based on the nuclear smoothing is obtained,and the progress factor and the settlement rate are randomly simulated,and the distribution of the outstanding claims reserve is simulated.A measure of the spread of the assessment data.Then,the fuzzy linear regression method is introduced in the case of the average compensation method,and the fuzzy regression equation is used to estimate the parameters by using the linear programming method and the fuzzy least squares method.The reserve evaluation results obtained by the two models are compared with the traditional payments per claim method evaluation results to verify the feasibility of the random method.And the payments per claim method based on the linear programming method to estimate the fuzzy linear regression parameters gives the width of the compensation amount for each accident year,and measures the random dynamic change of the uncertainty of the reserve.Finally,using MATLAB and R software to empirically analyze the above models,and get the corresponding conclusions.