caa a22 4500 386332576 CHVBK 20180307111720.0 cr unu---uuuuu 161130e198911 xx s 000 0 eng 10.2143/AST.19.2.2014908 doi S0515036100008485 pii (NATIONALLICENCE)cambridge-10.2143/AST.19.2.2014908 Ramsay Colin M. Actuarial Science, University of Nebraska, Lincoln NE, USA 68588-0307, (402) 472-5823. On an Integral Equation for Discounted Compound - Annuity Distributions [Elektronische Daten] [Colin M. Ramsay] 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). This is accomplished by assuming that N belongs to a new class of discrete distributions called annuity distributions. The probabilities in annuity distributions satisfy the following recursion: where an is the present value of an n-year immediate annuity. Copyright © International Actuarial Association 1989 Annuity distributions nationallicence integral equation nationallicence aggregate discounted claims nationallicence ASTIN Bulletin Cambridge University Press 19/2(1989-11), 191-198 0515-0361 19:2<191 1989 19 ASB https://doi.org/10.2143/AST.19.2.2014908 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2143/AST.19.2.2014908 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ramsay Colin M. Actuarial Science, University of Nebraska, Lincoln NE, USA 68588-0307, (402) 472-5823 NATIONALLICENCE 773 0- ASTIN Bulletin Cambridge University Press 19/2(1989-11), 191-198 0515-0361 19:2<191 1989 19 ASB CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge