As the actuary for a Lloyd’s syndicate specialising in property reinsurance, you are asked to quote a £3M xs £2M layer for a Risk XL policy, which is covering a portfolio mostly of large commercial properties. You are given the following risk profile for an insurer who insures its property risk.

MPL (lower limit) MPL (upper limit) Average in band, M Total premium 0 500,000 250,000 3,484,440 500,001 1,000,000 750,001 9,009,920 1,000,001 1,500,000 1,250,001 7,848,230 1,500,001 2,000,000 1,750,001 6,995,310 7,000,001 8,000,000 7,500,001 7,011,480 8,000,001 9,000,000 8,500,001 7,512,650 9,000,001 10,000,000 9,500,001 3,170,790 All amounts are in GBP You decide to use an exposure curve, some of whose values are tabulated below.

You can assume that the original loss ratio is 66%. Determine the expected losses to the layer, stating any additional assumption you need to make and interpolating the values in the table as necessary.

Priority/SI Swiss Re 3.0 Priority/SI Swiss Re 3.0 Priority/SI Swiss Re 3.0 2.0% 15.7% 36.0% 68.9% 70.0% 87.7%

4.0% 24.8% 38.0% 70.3% 70.0% 87.7%

6.0% 31.3% 40.0% 71.6% 72.0% 88.6%

8.0% 36.4% 42.0% 72.9% 74.0% 89.5%

10.0% 40.6% 44.0% 74.2% 76.0% 90.4%

12.0% 44.1% 46.0% 75.4% 78.0% 91.2%

14.0% 47.3% 48.0% 76.5% 80.0% 92.1%

16.0% 50.1% 50.0% 77.7% 82.0% 92.9%

18.0% 52.6% 52.0% 78.8% 84.0% 93.7%

20.0% 54.9% 54.0% 79.9% 86.0% 94.6%

22.0% 57.1% 56.0% 80.9% 88.0% 95.4%

24.0% 59.1% 58.0% 82.0% 90.0% 96.2%

26.0% 60.9% 60.0% 83.0% 92.0% 96.9%

28.0% 62.7% 62.0% 84.0% 94.0% 97.7%

30.0% 64.4% 64.0% 84.9% 96.0% 98.5%

32.0% 66.0% 66.0% 85.9% 98.0% 99.2%

34.0% 67.5% 68.0% 86.8% 100.0% 100.0%