A direct writer has a surplus reinsurance treaty with a maximum retention of 80,000 (there is no minimum retention level) and a maximum of 8 lines to be passed to the reinsurance.The following risks all gave rise to claims. In each case, calculate the range of possible amounts paid by the reinsurer to the direct writer. a) Risk 1 EML is 240,000 Claim amount is 12,000 Now if I assume that the direct writer retains 80,000/= of the risk, the claim amount liable to them will be 1/3*12,000=4,000 Meaning reinsurer pays 8,000/= which according to the answers given is correct. However, the second part of the question where we assume direct writer retains the least amount of risk says that reinsurer will pay 10,667/= How do we arrive at this answer
If the direct writer retains the least then it must use all of the available lines (ie 8). Remember the number of lines is the ratio of the amount ceded to the amount retained. Hence the direct writer must retain 1/9th of the risk and therefore cedes 8/9ths. For a claim of 12,000 the recovery from the reinsurer is therefore 8/9*12,000=10,667
