Recursions for multivariate compound phase variables

We show how to generalize the result given in [Eisele, K.-Th., 2006. Recursions for compound phase distributions. Insurance: Math. Econom. 38, 149-156] to the multivariate case, i.e. we find a Panjer-like recursion principle for the distribution of a multivariate compound phase variable. Recursion formulas and procedures for the bivariate case are given in detail. We give a possible application for agricultural risks and calculate concrete examples via a VB-program.