Fall 2018 Q13 part a.ii)
Hi Graham - The question asks for rate per $1000 which is generally pretty straight forward. This particular question introduces a curveball with a loss distribution that varies per interval. I understand it except for part a) ii) where we have to assume the AOI = $800K. I don't understand the calculation of the $766.67 in the average severity calculation for the 700K < X < 850K interval from the examiner's report. I get why the average severity is calculated different but I don't understand how it's calculated. I thought it would be $750K instead by doing (700+800)/2 but that's wrong. Can you help me think through this? Perhaps it will make the linear interpolation component below make more sense. Thanks.
Avg Severity = .5(200K) + .25(475K) + .1(625K) + .1(766.667K) + (.025 + .025)(800K) = $397.917K
Where 766.667K from above is calculated: 750K*(2/3)+800K(1/3)
Comments
Hello @brb2241
I'm sorry I didn't see your question until today. I will provide an answer sometime Friday.
@Graham
The trick here is that to calculate the average severity in the larger interval (700, 850), you have to break that interval into 2 smaller intervals as follows:
The reason the breakpoint is 800 is that AOI = 800 for part (ii). Then:
Then you have to observe that for all losses that fall in the larger interval (700, 850), we would have 2/3 of them in the interval (700, 800), and 1/3 in the interval (800, 850) - because the severity distribution is uniform. From there you can calculate the average severity for (700, 850) as a weighted average:
If the AOI in part (ii) had fallen on the end of one of the intervals for the size of loss distribution (Ex: 850) then you wouldn't have had to do that. But since it fell in the middle, you had to do the extra step as explained above.
Got it, thanks!
You're welcome! 😀