In an earlier paper the author derived a recursion formula which permits the exact computation of the aggregate claims distribution in the individual life model. To save computing time he also proposed an approximative procedure based on the exact recursion.

In the present contribution the exact recursion formula and the related approximations are generalized to the individual risk theory model with arbitrary positive claims. Error bounds for the approximations are given and it is shown that they are smaller than those of the Kornya-type approximations.

It is shown how the upper bounds for stop-loss premiums (and approximations to tail probabilities) obtained by replacing the individual model for a portfolio of risks by the collective model can be improved upon at the cost of only slightly more computer time. The method used is simply to keep a restricted number of large risks as they are instead of approximating them by a compound Poisson distribution. In a real-life example, the relative error in the stop-loss premium is shown to be reduced drastically by keeping only 10 out of 743 risks unchanged.

We compare three modern methods for calculating the aggregate claims distribution with respect to their computation amount and accuracy: Panjer's algorithm, the approximation method of Kornya and the most recent, exact procedure of De Pril. They are compared numerically in the case of actual Life portfolios. The computation amount of De Pril's method is much greater than that of the two others, which do not differ substantially in this respect. The accuracy of Kornya's and Panjer's methods is remarkably high in the examples considered. However, as the accuracy of Kornya's approximation method can be determined easily in advance, this procedure turns out to be the most useful one for the problems arising from practical work.