On the distributions of two classes of correlated aggregate claims

We consider two classes of correlated aggregate claims distributions, one with univariate claim counts and multivariate claim sizes and the other with multivariate claim counts and univariate claim sizes. We show that when the multivariate claim counts distribution takes a certain form the second class of multivariate compound distribution reduces to convolution of a number of compound distributions in the first class. (C) 1999 Published by Elsevier Science B.V. All rights reserved.