Chap 20 - Reinsurance layer for exposure rating

Hi all,

I hope you're well.

I'm studying using the CMP for the 2021 exams so apologies if the content I'm referring to has been removed/amended in the 2023 CMP.
In the 2021 CMP chapter 20 section 3 (Derivation of risk premium for P&C per-risk non-proportional) and paragraph titled "Basic exposure rating using ILFs", it is mentioned that

"the reinsurer will need to use (calculate) the 100% limit (L) and the excess (E). [...] Suppose also that a reinsurance layer with limit LR and excess ER is being priced"

Then the formula provided is "Proportion = [ILF(LR + ER) - ILF(ER)] / [ILF(L+E) - ILF(E)]" with some modifications such as the need to amend this formula with 0 if the reinsurance layer finishes below the risk.


1. Maybe I'm biased by 3+ years in reinsurance pricing but I would have thought that the formula would need to account for the reinsurance layer being on top of the original policy conditions.
In this case, the reinsurer would incur losses if (and only if) the original insured claims for more than ER + E (as the first E is retained by the insured, then the next ER is retained by the insurer, and everything above is passed onto the reinsurer, subject to the limit of LR).
So the formula would need to account for a term ER + E somewhere. Likewise, a term LR + ER + E would be required for the exit point of the reinsurance layer.

And regarding the fact that the loss to reinsurer would be 0 if the reinsurance layer finishes below the risk, this would be invalid using the below example:
- original conditions are 20 xs 10
- reinsurance layer is 7 xs 3

The reinsurance layer exits at 10 which is the entry of the original policy, so this falls in the scope of the consideration. But this reinsurance layer would in fact be a 7 xs 13 in regard of losses sustained by the original insured, so if there is a claim for 15, the insured retains 10, passes 5 onto its insurer which recovers 2 from the reinsurer.


2. An alternative interpretation for the reinsurance layer is that it is simply not 'stacked' on top of the original policy. This means that the reinsurance layer is LR xs ER in regard of losses sustained by the original insured, not by the insurer.
In this case, I fully agree with the formula, chart and modifications.

However, it's not what I'm used to seeing in my work hence why I'm asking for some clarifications.
Also, intuitively, we would expect the reinsurance layer to apply to losses borne by the cedant, not by the original insureds.


I'd be grateful if someone could help me clarify this section please.
Looking at the last 3 years' past papers, it looks like numerical exposure rating questions have never (ever?) included original deductibles/excesses ie original policies were primary limits. So original deductibles were never a problem, but I thought it'd be worth asking as a just in case.

Thanks