"We should consider the impact of large losses. If we do not adjust for the impact of large losses, we may obtain a misleading severity pattern and assume inappropriate severity trends. Approaches include: basing the trend on the historical median rather than mean values. " Can you please explain with an example, what does it mean?
Large losses will probably be subject to different trends than attritional claims, eg different inflationary trends. (I can imagine for example that large losses are more exposed to court awards and medical costs than are attritional claims.) Therefore if we include large losses in our ACPC data, we will be overestimating claims inflation. However, the median claim won't be affected (or not significantly anyway). Let's see an example. Imagine you have 100 claims, consisting of 99 attritional claims of £1 each, and one large loss of £1000. the mean of all claims is £10.99 and the median is £1. if we exclude the large loss, the mean is £1 and the median is £1. So you can see that the large loss distorts the mean (because it includes information about the size of losses), but it has no effect on the median. This is because the median doesn't care HOW BIG the large loss is, it only cares HOW MANY losses are to the left or the right of the 50th percentile.
