Hi, Ref: CMP, Ch20, p.10 (Question 10.6) A couple of questions about the solution to this question: - First paragraph: Isn't the cost of cover the excess of guaranteed claim amounts over asset shares, not just total claims payments? - Could you elaborate on the second paragraph please? This seems a cumbersome way to do this but more importantly, when it says "calculate the cost of cover using these smooth rates", could you describe this process please?
1. No, the cost of cover when looking at the asset share for the cohort is the total claims paid (but using the excess of claims over asset shares can be used for per policy asset shares). An example may help. Imagine a cohort of business with 10 policyholders and an asset share for the cohort of 100. The asset share per policy is then 10. If one policyholder dies and is paid 19, then we now have a cohort asset share of 81. Dividing this between the survivors gives a per policy asset share of 9. Alternatively, we could deduct the excess of the claim over the asset share (19 - 10) and share it between the survivors, ie 10 - (19-10)/9 = 9. 2. Yes, it is cumbersome, but we'd get very erratic answers if we didn't smooth the mortality cost. Take an extreme example where there are two 85 years olds and two 86 year olds. One of the 85 year olds dies. We then have a mortality rate of 50% at 85 and zero at 86. It may be that on average, this represents a mortality rate of 20% more than we expected using the latest tables. So one approach could be to base our asset share calculations on 120% of the rates in the tables (as the tables have already been smoothed). Best wishes Mark
