Inequalities for the De Pril approximation to the distribution of the number of policies with claims.

In the present paper, we give su¢ cient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A numerical example is given.

On multivariate Vernic recursions

In the present paper we extend a recursive algorithm developed by Vernic (1999) for compound distributions with bivariate counting distribution and univariate severity distributions to more general multivariate counting distributions. IA. Panjer (1981) described a procedure for recursive evaluation of a compound distribution when the counting distribution belongs to a certain class. Vernic (1999) developed a bivariate version of this recursion, assuming that the counting distribution is bivariate and the severity distribution