Some Bounds of Outstanding Claims Reserve Distribution by NBUE

In order to solve the reserve problem of the insurance company, this paper studies the Outstanding Claims Reserve(OCR) distribution function by establishing their queuing models. When the claim distribution is NBUE class, we use the character of the distribution class to analyze the OCR distribution. So we obtain some useful upper bounds and lower bounds of the OCR distribution by the mean and variance of the claim. Furthermore, we also give an example to illustrate the approximate effect of these bounds. This empirical results show that these bounds of the OCR are approximated to the truth and redound to reserve equal OCR for the insurance company.