On the distribution of a sum of correlated aggregate claims

Assume that a book of business is the union of disjoint classes of business and each of which has an aggregate distribution. The classes of business are correlated. We present necessary formulas to compute the aggregate distribution for the whole book when claim counts distribution takes a certain form. As a special case when claim counts distribution is multivariate Poisson, we show that the aggregate distribution for the whole book is compound Poisson.