Conditional recursive equations on excess-of-loss reinsurance

The marginal recursive equations on excess-of-loss reinsurance treaty are investignted, under the assumption that the number of claims belongs to the family consisting of Poisson, binomial and negative binomial, and that the severity distribution has bounded continuous density function. On conditional of the numbers of claims associated with the reinsurer and the cedent, some recursive equations axe obtained for the marginal distributions of the total payments of the reinsurer and the cedent.