Between Individual and Collective Model for the Total Claims

This article studies random variables whose stop-loss rank falls between a certain risk (assumed to be inter-valued and non-negative, but not necessarily of life insurance type) and the compound Poisson approximation to this risk. They consist of a compound Poisson part to which some independent Bernoulli-type variables are added. Replacing each term in an individual model with such a random variable leads to an approximating model for the total claims on a portfolio of contracts that is computationally almost as attractive as the compound Poisson approximation used in the standard collective model. The resulting stop-loss premiums are much closer to the real values. Reinsurance Research - Loss Distributions, Size of