Has anyone had a stab at assignment 4 question 5? I can get the expired and unexpired risk units (sum = 168) but I can't follow the solution for working out that it's this multiplied by 7/48. I can understand why it's 7m but I can't work out how to get the 48 risk units.
48 is the sum of risk units prior to October - there's a 3 month delay. See 4th and 5th para on p10 of the solutions.
I can't seem to understand the part of the solution at the end of p9. My workings are as follows Month Risk Unit per Month 1 1.5 2 1.5 3 1.5 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1.5 Sum 14 Month Expired Risk 1 14 2 12.5 3 11 4 9.5 5 8.5 6 7.5 7 6.5 8 5.5 9 4.5 10 3.5 11 2.5 12 1.5 Sum 87 So in my view the 7m claims paid refer to 79.5 (adding ER from 1-9) expired risk units.
I don't quite follow what you've done, but in your first list of risk units per month, you seem to have missed the fact that policies written in January will also expose in February, so there are 3 risk units in February for example.
The first table gives how much a single policy is exposed to per month. So for example a policy written in January will have been exposed to 14 risk units by the end of the year. Likewise a policy written in February is exposed to 1.5 risk units in that month, 1.5 units in March, 1 unit in April etc so expired risk units would be 12.5 for this risk by year end.
In that case your table is not comparable with the table in the solution, so you can't just add the same months. In the solution, we show the total exposure during each month. You add these (months 1-9) to get the expired exposure in respect of paid claims, ie 48. What you've done, is calculate for each month's policies, the exposure by the end of year, then taken months 1-9. This isn't the same thing, because you, for example, have included exposure in December for policies written in January in your calculation!
