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April 2000 q5 - motor fleet credibility

N

NatalieB

Member
Hi,

Wondering if anyone can help me understand the examiner's comments on this question - part iii

They say that the average number of claims for the business is 20 percent which I assume is just market average for motor fleet. However they then go on to say the standard deviation is around 16 claims - struggling to see how they get that. Are they using an approx distribution?

They then say that the 65 percent credibility factor may therefore be thought to be inappropriate. Is that because there is too much variability and thus it is too high?

If anyone can help me out I would be very grateful
 
Hi Natalie,

Yes, this part of the solution is not very clear!

Like you, I think 20% has been chosen as a market average claim frequency for Motor Fleet (although I think it's probably a bit higher than that these days).

For the standard deviations, we haven't been given the actual numbers of claims, so would need to use a proxy to estimate the variation in claim numbers. The sample standard deviation (using n-1) of the numbers of vehicle years is 15.8 (and we could maybe assume that the claim number distribution follows a similar pattern to the exposure). The equivalent standard deviation from the grossed-up claims amounts is 17.4, which is also close to 16. So this could be where the estimate of 16 has come from ...

For this number of claims and level of variability, the 65% credibility is likely to be too high.

[If you would like a definitive answer to the standard deviation issue, I'm happy to check back with the Institute for you, but can't guarantee to have an answer before your exam.]


Coralie
 
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