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Percentile

J

JeanOlivier

Member
Hi,

I wanted to know what is meant by claims reserves set at 75th percentile of the range of possible future outcomes. Is it the probability that there is a 75% probability that the claims will be equal to this? How is reinsurance taken into account in this? What about claims set on a best estimate basis? Is it the mean of the scenarios ie 50% percentile? Is my interpretation correct?

Thanks.
 
Here's what I think. Could be wrong!

JeanOlivier said:
Is it the probability that there is a 75% probability that the claims will be equal to this?
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I think this is a 75% probability that the claim reserves will be below this value.

What about claims set on a best estimate basis? Is it the mean of the scenarios ie 50% percentile? Is my interpretation correct?
Click to expand...

You are confusing mean and median. the median is the 50th percentile. The mean (average of all possible outcomes) doesn't have to be the 50th percentile. Usually claims reserves will be negatively skewed so the mean will be higher than the 50th.

Best estimate is whatever the company defines that to be (I think) - but should really be the mean.

How is reinsurance taken into account in this?
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That's a bit more complicated and depends how you are creating your range of reserves. I'll leave that to someone more knowledgeable!
 
Thanks for your kind help.

In the April 2008 question 1 (vii) examiner's report, the explanation for the 90th percentile is interpreted as "one in ten years, we might expect ultimate to be greater than 90th percentile". Is this another way of saying that there is a 10% chance that the ultimate claims will be higher than the 90th percentile?
 
JeanOlivier said:
In the April 2008 question 1 (vii) examiner's report, the explanation for the 90th percentile is interpreted as "one in ten years, we might expect ultimate to be greater than 90th percentile". Is this another way of saying that there is a 10% chance that the ultimate claims will be higher than the 90th percentile?
Click to expand...


Yes. Although I think some people get uncomfortable with turning percentiles into return periods (i.e. one in ten etc.) as non-technical people sometimes interpret, e.g., 1 in 100 to mean it won't happen for 100 years.
 
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