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Sep 2006 Q8 (iii) and (iv)

J

Jiang

Member
A bit last minute.

For part (ii), I can work out the mean and standard deviation of the lognormal. But the solution at the end of that part says "if working in £, mean of A is 17.16, etc". How are these number calculated?

For part (iv), I can work out the 99.5 percentile for the distribution, but to translate this to claim amount, I am a bit clueless.

Thank you very much for your help.
 
In (iii), the solutions work in £ms but you could work in £s instead.

So, for Motor, instead of mean = 30.00, you would have mean = 30,000,000.
If you work through the numbers, you find that s = 10,000,000 and so CV is unchanged at 0.33.
sigma is also unchanged at 0.32 but now, log(mean) = 17.217 because you are using a different number for the mean, so your value for "mu" will be different.

In (iv), again using Motor as an example, the 99.5th percentile for the underlying normal distribution is 4.1846 (rounded to 4.19).
But the claims are lognormal so we would need to take the exponential.
e to the power of 4.1846 is 65.67.
 
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