Measuring the Effects of Reinsurance by the Adjustment Coefficient

In this paper we consider the optimal levels of reinsurance in cases where the cedent has a choice between a pure quota-share treaty, a pure excess of loss treaty or any combination of the two. The optimality criterion that we use is that the insurer's adjustment coefficient should be maximized, subject or not to a constraint on the insurer's expected net profit. The solution is given, assuming that the claims have a compound Poisson distribution, that the quota-share premium is calculated on a proportional basis with a commission payment and that the excess of loss reinsurance premium is calculated according to the expected value principle.