Correction to Introduction to Reinsurance, Study Note ERM-114-13
The examples on Page 12 contains an incorrect analysis for Example 2. For stop-loss reinsurance, the priority (deductible) is first exhausted and then the copayment applies to the excess. The example has a priority of 80% of the premium, a capacity (maximum to be paid by the reinsurer) of 20%, and a copayment of 25%.
Example 1 – claims are 70%. The priority reduces the reinsurer's obligation to 0. The insured pays the full claim.
Example 2 – claims are 100%. The priority reduces the reinsurer’s obligation to 20%. The copayment reduces it to 0.75(20%) = 15%. This is below the capacity, so the reinsurer’s share is 15% and the insured pays 85%. (It appears the author used 20% as the copayment)
Example 3 – claims are 115%. The priority reduces the reinsurer’s obligation to 35%. The copayment reduces it to 0.75(35%) = 26.25%. This is above the capacity, so the reinsurer’s share is 20% and the insured pays 95%. (Adding the amounts allocated to the cedant by the author, 80 + 6.67 + 8.33, produces the same result).