Hello there, I have read the ASET solution to the part of this question that relates to 'treaty B' and have the following question: ASET mentions that it seems sensible to assume that the risk premiums are paid to the reinsurer annually in advance (ie, at the same time as the insurer receives the retail premium), but when calculating the EPV(reinsurance premiums) the ASET solution includes the factor v^1/2. Does the inclusion of this factor not mean that we're assuming we pay the reinsurance premiums half way through the year? Also, the question says that the treaty B reinsurance premiums are annually renewable, but in the solution we make use of the fact that q(x)^r = q(x)^p * 1.1. Does using this relation not assume that the risk premiums are guaranteed (and not reviewable)? Thanks, Matt
Hi Matt Can I just check we're looking at the same thing here - ASET solution, top of page 10 of that sitting's solutions, the formula for EPV {reinsurance premiums} doesn't have any v^1/2 factors as I see it? I'm reading EPV {reinsurance premiums} = RP(50) + RP(51) v p(50) + ... Apologies if I'm missing the point of your query - of course please let me know if so! The solution is using q(x)^r = q(x)^p * 1.1 because the question tells us the Treaty B risk premium rates are based on the insurance company's original pricing assumptions plus a 10% loading. (The fact that the treaty is renewed (or not!) annually is a different issue.) Lynn
Hello Lynn, Thanks very much for your reply. Yes, that's it, the top of page 10. I was actually looking 4/5 lines down from the one you're looking at - there's a v^1/2 factor just after the bracket. But even looking at the line that you're looking at (the summation of RP's) each RP contains a v^1/2 factor - which is noted on the previous page. And regarding the 10% loading, I understand that the question says that the reinsurer uses a 10% loading, but the question also says that the reinsurer's rates are reviewable. These two statement seem to be mutually exclusive, which is why I'm confused. Thanks, Matt
Hi Matt Ah, ok - I'm with you now The v^1/2 factor in each RP is because the RP is being calculated as the PV of the expected claim cost (so is discounting for half a year assuming deaths benefits paid half way through the year on average). The v^1/2 is nothing to do with the timing of the reinsurance premium - these are assumed to be paid annually in advance. Does that help sort it? The question says that the Treaty B is annually renewable, it doesn't say that the reinsurer's rates are reviewable. So, if the reinsurance is renewed each year, the reinsurance premium will change (eg as policyholder age increases) but the risk premium's being used to determine the premium will remain unchanged. Hope this reply helps clarify Lynn
Hi Lynn, I'm sorry for not responding sooner. Yes, both parts do now make sense - I didn't realise that I was mixing up the words renewable and reviewable. Based on your response I think I might have also been using the words reinsurance premium and risk premium incorrectly. To double check, is it the case that a reinsurance premium is a monetary amount, whereas a risk premium is a fixed formula used to determine the reinsurance/monetary premium. Thanks, Matt
A follow on from the above, having read the solution to part iv) which (under the "Additional points") says that "if experience improves in future, risk premium rates could fall, increasing the insurer's profits". Please could I clarify what's meant here. Above, and also in the question wording, it says that that the risk premium is fixed and based on the insurer's original premium basis. Since it's based on the original basis then in my mind whether or not experience turns out better or worse than expected can't have an affect on the reinsurance premium (as the risk premium formula is fixed and based on the original basis)? So is the solution correct? The only way I can make sense of the solution is if it means that, given treaty B is annually renewable, we don't renew and instead negotiate a better treaty in light of the improved experience?
Hi Matt Yes a risk premium is a way to calculate the reinsurance premium (which will be a monetary amount). An alternative way to calculate the reinsurance premium is as a percentage of the insurer's premium. Best wishes Mark
Hi Matt I agree, the question wording isn't totally clear. But yes, if the insurer didn't renew then it could benefit from whatever new cheaper rates were available. Best wishes Mark
