On the single case of probability distribution for total insurance payments in the problem of excess-of-loss reinsurance

We consider a problem of finding of probability distribution for total insurance payments when excess-of-loss reinsurance is used. The problem is considered in the case when losses in each insured accident have uniform distribution. The main result is analytical expression of probability distribution function for total payments. This result can be used to estimate a precision of optimal retention limit calculation based on normal approximation.