Hi, This is probably really simple - in chapter 15 the text reads: The recoveries from the reinsurance contract will differ depending on whether the different layers (of the same risk) written by the cedant are regarded as stacked or independent within the terms of the XL reinsurance treaty. For example, suppose that layers 400k xs 100k and 1m xs 500k are written by the cedant and a reinsurance contract for 500k xs 500k covers these contracts. If the layers are stacked, then the underlying contract is essentially 1.4m xs 100k and the reinsurance covers the range [600k,1.1m]. If they are independent, the reinsurance only affects the 1m xs 500k contract, covering the range [1m, 1.5m]. I am not sure I completely follow the last range of [1m, 1.5m] - if the layers are independent, I can follow that the reinsurance only affects the 1m xs 500k contract, but why does it then only affect the latter proportion? Is that just basically because the reinsurance will cover the top proportion of the layer, rather than from the attachment point. Thanks very much!
Yes that’s right. If the layers are independent then the reinsurance only protects the 1m xs 500k contract because you need a loss of greater than 500k in order to hit the reinsurance layer due to the attachment point of 500k on the reinsurance contract. The layer 1m xs 500k covers the portion of ground-up losses from 500k to 1.5m. Hence a reinsurance layer of 500k xs 500k protecting this layer will be covering the portion of ground-up losses from 1m to 1.5m.
