caa a22 4500 388071184 CHVBK 20180307125149.0 cr unu---uuuuu 161130e199911 xx s 000 0 eng 10.2143/AST.29.2.504617 doi S0515036100012605 pii (NATIONALLICENCE)cambridge-10.2143/AST.29.2.504617 Sundt Bjørn University of Bergen Discussion on D.C.M. Dickson & H.R. Waters Multi-Period Aggregate Loss Distributions for a Life Portfolio [Elektronische Daten] [Bjørn Sundt] In the present discussion we point out the relation of some results in Dickson & Waters (1999) to similar results in Sundt (1998a, b). We shall need some notation. For a positive integer m let m be the set of all m × 1 vectors with positive integer-valued elements and m+ = m ~ {0}. A vector will be denoted by a bold-face letter and each of its elements by the corresponding italic with a subscript denoting the number of the elements; the subscript · denotes the sum of the elements. Let m0 be the class of probability functions on m with a positive probability at 0 and m+ the class of probability functions on m+ . For j = 1, , m we introduce the m × 1 vector e j where the jth element is one and all the other elements zero. We make the convention that summation over an empty range is equal to zero. Let g ∈ m0 be the compound probability function with counting distribution with probability function v ∈ 10 and severity distribution with probability function h ∈ m+; we shall denote this compound probability function by v V h. Sundt (1998a) showed that where φv denotes the De Pril transform of v, given by Motivated by (2) Sundt (1998a) defined the De Pril transform φg of g by This defines the De Pril transform for all probability functions in m0. Insertion of (2) in (3) gives and by solving φg(X) we obtain Sundt (1998a) studies the De Pril transform defined in this way and found in particular that it is additive for convolutions. Copyright © International Actuarial Association 1999 ASTIN Bulletin Cambridge University Press 29/2(1999-11), 311-314 0515-0361 29:2<311 1999 29 ASB https://doi.org/10.2143/AST.29.2.504617 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2143/AST.29.2.504617 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sundt Bjørn University of Bergen NATIONALLICENCE 773 0- ASTIN Bulletin Cambridge University Press 29/2(1999-11), 311-314 0515-0361 29:2<311 1999 29 ASB CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge