Q18.6 Credibility Theory - Answer Wrong?

Hello!

I hope this is the case, because if it's not I'm really missing something with this part of the course!!!!

Question:

Assume:
Claim Frequency follows a Poission.
Individual Claim Sizes follow a log normal with mean 100 and Standard deviation 250.

Need to be 90% sure that the observed mean claim size will not differ from the underlying mean claim size by more than 5%. How many observed claims are needed to assign full credibility?

The answer works out the frequency full credibility as 1,082, which makes sense. Now, from what I understand they should then multiply this by (250/100)^2 as we know the mean and SD of the log normal. However, in the answers they calculate the paramaters of the log normal and use these values instead. Is there something I am completely missing that explains why do this done?

Thank you for any replies that people give to this and I wish you all the best of luck come the exam!!!!!!!

 

Well, I haven't seen the solution so this is a bit of a shot in the dark.

By finding mew and sigma they have found the mean and sd of the underlying normal distribution. Do they then just solve that to get the same final answer?

I would have thought it should return the same answer although I haven't checked it.

Let me know if this makes sense.

 

Hi,

Thanks for the quick reply. It's much appreciated!

The solution calculates CV = [(1.981)^(1/2)] / 3.61467 = 0.38938. This all comes from the parameter values of the log normal.

Where as if you use the actual mean and standard deviation of the log normal, that are given in the question, CV = 250/100 = 2.5.

So the final answers come out completely different.

The bit that confuses me with the answer in the notes is that they are working out the parameters for the distribution, which in this case happen to be a mean and variance of a normal distribution, but this normal distribution has no rellevance to the question as far I can see. Also, if we were to use a Gamma distribution then we wouldn't back calculate it's parameters as they would be meaning less so surely it should not be done for the log normal either?

Does this makes sense or is there something that I am completely missing with their methodology?

Thanks again for your reply and let me know if any of this doesn't make sense

 

Thank you

Thank you for that. It seems strange that the corrections were taken down before the 2010 exams have finished though. Surely it would make sense for acted to leave the corrections up until the end of this sitting?

Thanks again for posting though!

 

Perfect! Whenever I've looked for the corrections I've always got to the links for the 2011 ones that just say that there aren't any for any of the subjects!

Thank you!