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in BUS 4027W - Actuarial Risk Management by
For individual surplus, I understand that the insurer pays (Retention limit/EML) x Claim or  (Retention limit/Sum insured) x Claim.

What happens if the reinsurer states there is a maximum retention limit and a minimum retention limit? I'm assuming that you always use the maximum retention limit unless the EML or Sum insured is below this retention limit, then the minimum retention limit would be used. This would benefit the insurer right?

Please let me know if the above explanation is right!
by (4k points)

Hi Anonymous

I think you may be getting confused between individual surplus and normal surplus reinsurance. As far as I am aware there are no situations in which an individual surplus contract would be specified with an upper and a lower limit. If you have a specific example which you came across, please post it and I will go from there.


by (680 points)

This is taken from the 2015 paper 1 Q1: The question does the calculation for iii) using the maximum retention limit for the individual surplus. It then uses the minimum retention limit to calculate the maximum possible reinsurance amount for iv (I left out the table because it did not fit).

ARM Exam 1 - 2015.docx (50 kb)

ARM Exam 1 Sch - 2015.docx (78 kb)

PropSure has set up reinsurance treaties which operate in the order given below:

25% Quota Share treaty with Reinsurer A.

Individual Surplus with Reinsurer B, which has a maximum retention limit of $50m and which stipulates that PropSure must retain at least $10m on each risk reinsured

Individual Risk Excess of Loss with Reinsurer C, providing cover of $5m in excess of $2m
(iii) Determine the amounts (a) – (e) in the above table.
(iv) Derive, and simplify, an expression for the maximum recovery (from an individual claim of L on a policy with sum insured S) which could be made from the proportional treaties, in terms of L and S.

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by (4k points)

Thanks for the info NatanK

Questions like these do not portray the usual situation. Ie. In practice there would not normally be a minimum retention for an individual surplus arrangement. However, part iv of this question requires this information specifically, and that is why it is given. For your normal calculations, it does not affect anything as the retention is specified for both of the claims at $50m.