Combining Quota-Share and Excess of Loss Treaties on the Reinsurance of n Independent Risks

In this paper, we seek to find the optimal retentions of an insurance company which intents to reinsure each of n risks belonging to its portfolio by means of a pure quota-share treaty, a pure excess of loss treaty or any combination of the two. The criterion chosen to the selection of the optimal program is the maximization of the adjustment coefficient, attending to the relationship existing between this coefficient and the ruin probability.