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FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans

A reinsurer has an excess-of-loss treaty with an insurer: the reinsurer pays 100% of each loss above 5 million, up to a limit of 20 million per loss (that is, covering losses between 5 million and 25 million). The insurer suffers three separate losses of 3 million, 12 million, and 40 million. How much does the insurer retain in total after reinsurance?

The insurer retains 28 million. The 3 million loss is fully retained, the 12 million loss leaves 5 million retained, and the 40 million loss is covered only up to 20 million, so 20 million is retained. The total is 3 plus 5 plus 20, which equals 28 million.

  1. A20 million
  2. B28 millionCorrect
  3. C30 million
  4. D48 million

Explanation

Loss of 3 million: below attachment, retained 3 million. Loss of 12 million: reinsurer pays 7 million, retained 5 million. Loss of 40 million: reinsurer pays capped 20 million, retained 20 million (5 retention plus 15 above the 25 million cover). Total retained = 3 + 5 + 20 = 28 million. Choosing 30 million would wrongly cap retention at 5 million on the large loss plus other errors; 20 million ignores the first two losses and the cap interplay.

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