Measuring the impact of dependence between claims occurrences

The purpose of this paper is to provide a quantitative measure of the impact of a possible dependence between the occurrences of claims in an individual risk model. Firstly, probabilistic distances, of stop-loss or total variation types, specific to arithmetic random variables are introduced and studied, especially in connection with related probabilistic orderings. Then, these results are applied to derive effective bounds for the distance between the total number of claims in the original model and under a standard independence assumption.