On Multivariate Panjer Recursions

Abstract

Abstract In the present paper we generalise Panjer's (1981) recursion for compound distributions to a multivariate situation where each claim event generates a random vector. We discuss situations within insurance where such models could be applicable, and consider some special cases of the general algorithm. Finally we deduce from the algorithm a multivariate extension of De Pril's (1985) recursion for convolutions.