Actuarial Outpost Adjusting ultimate losses for actual length of period
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#11
11-01-2010, 10:32 AM
 Utanapishtim Member CAS Join Date: Jan 2004 Location: BC Posts: 3,088

I still think it's higher. Let's have another look at the figures:
1m losses developed to 52.75 days = 100%
1m losses developed to 21.75 days = 52.4%
So, 1m losses emerging from 21.75 to 52.75 days is 47.6%; of which how much emerges between 21.75 and 25 days?

The proposed answer is that if 47.6% emerges over 31 days, then 1.5355% emerges each day, and so 3.75x1.5355% = 4.99% emerges by day 25.
I say the answer is more than 4.99%, because of the mechanics of the loss emergence. I believe it was said that this is personal auto. From day 21.75 until at least day 28, there are still accidents occurring in month 1. Because they are car accidents, they are likely to be reported very quickly (and thus case reserved), as people will want to get repairs done and get back on the road. Several days after the end of month 1 (but well before day 50), new reports should be trickling off, and so the pure IBNR emergence should clearly be front-loaded. To the extent that original reserves are inadequate on average, there will also be some case development - this should be less front-loaded, and may even be back-loaded as MH suggests, but is probably of secondary magnitude to the pure IBNR emergence.
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