Q& A Bank part 6 Q 6.12 - Accounting

could someone please give me an explanation for this solution - I'm completely confused as.

1. Premiums written uniformly over year - hence mid year inception on average.
2. Claims incurred evenly over each year - hence claims occur on average at yr end.
3. Assume that 50% of claim amount is paid exactly 3 months after claim incurred , 20% after 9 months , 15% after 18 months and remaining 15% after 36 months.

Solution given: take's one years business - and calculates reserve at end of year of sale.
At end of year - 0.25 of payments at 3 months are outstanding due in 1.5 months on average ???? Surely these payments would occur at duration 15 monts - i.e. due in 3 months - with no payments made inside 1st year of sale .???

Thanks for help

 

The solution is using an accident year approach. It assumes that claims are spread evenly over the year, but doesn't assume that they all occur mid-year (although they will on average). Then it can allow for the fact that the only the 3-month claims that occur after 1 Oct will still be outstanding at the year end. All those occuring before 1 Oct will be settled before the year-end.

(If you assumed all claims were mid-year, you wouldn't have any of the 3-month claims outstanding.)

You are trying to use an underwriting year approach. I think this is feasible. Not thought that hard about it. You could assume all claims year end, but you need to make sure you allow for enough UYs. Perhaps less accurate since if you try to avoid making the "on average" assumption it's a bit more messy as total exposure isn't uniform with time.