Some Remarks on the Cedent’s Retention Risk in Presence of an Annual Aggregate Deductible or Reinstatements

We observe on the market that a lot of excess of loss reinsurance treaties have specific clauses such as an annual aggregate deductible or reinstatements. These clauses imply that the aggregate claims of the ceding company not only depends on the company’s own retention but also on the aggregate claims of the reinsurer. Theses risks are obviously dependent. This is our motivation for looking at multivariate extensions of the collective risk model in this paper. It will give us the necessary tool for the exact evaluation of the cedent’s retention risk in excess of loss covers with an annual aggregate deductible or reinstatements. The importance of working with these multivariate extensions will be tested by comparing the exact results, calculated in the multivariate model, with the approximated results in the wrong (under the false assumption of independence) univariate case.