We consider a risk generating claims for a period of N consecutive years (after which it
expires), N being an integer valued random variable. Let Xk denote the total claims
generated in the kth year, k≥ 1. The Xk's are assumed to be independent and identically
distributed random variables, and are paid at the end of the year. The aggregate discounted
claims generated by the risk until it expires is defined as where υ is the discount factor. An
integral equation similar to that given by Panjer (1981) is developed for the pdf of SN (υ) …