Estimation Of Outstanding Claims Reserve Based On Fuzzy Queuing Systems

Estimating the reserve for outstanding claims is one of the most important tasks in the actuarial business of insurance.It is mainly to estimate the reserves for two types of projects: one is the amount of claims that have occurred in cases that have not been reported to the insurance company,and the other is the amount of claims that have been reported to the insurance company but have not been paid.In recent years,with the increase of uncertainties in the market,scholars have begun to introduce the idea of fuzzy mathematics into the estimation method of outstanding compensation reserves,and come up with a new estimation method.According to the connection between the outstanding claims reserves and the fuzzy queuing system,it can be seen that the distribution of outstanding claims reserves is related to the number of outstanding cases,the processing time of each case,and the amount of claims for each case.Therefore,in this paper,considering the nature of the distribution function of the number of outstanding claims and the total service time,the uncertainty of the parameters in the distribution function is considered when estimating the reserve of outstanding claims.Firstly,This paper considers that the number of policy losses is the Poisson flow,and the total time distribution of loss report and compensation time is the negative exponential distribution.Two classical fuzzy queuing systems: FM/FM/1/? and FM/FM/c/? are established,based on Based on the theory of fuzzy structural element and the analysis method of fuzzy queuing mathematical model,the estimated value of the reserve for outstanding claims and the corresponding membership function are obtained.Meanwhile,the membership functions of the estimated value of the outstanding claims reserve under two different forms of fuzzy number are considered.Furthermore,when there is only one reimbursement officer,the total time distribution of loss report and compensation time is general distribution.Two fuzzy queuing systems: FM/G/1/? and FG_eo/G/1/? are established,and the corresponding estimated value and membership function of outstanding compensation reserve are obtained.Finally,paper based on the fuzzy queuing system: FM/FM/2/?,two different forms of fuzzy numbers are taken as examples to calculate the estimated value of theoutstanding claims reserve and the corresponding membership function.By comparing two examples with the estimated value of the outstanding claims reserve calculated by the queuing system based on fixed parameters,it shows that the fuzzy queuing system can estimate the outstanding claims reserve more comprehensively.