The general picture is that premium is increasing 30% a year, so IBNR is also
increasing 30% a year. IBNR is 10% of Premium. Premium increases from 10M to
13M to 16.9M and IBNR from 1M to 1.3M to 1.69M.
In the second year, suppose IBNR comes in at 1.5M instead of 1.3M. This
>could< be an increase from 10% of premium to 11.54% of premium. Then your
IBNR in the third year would be 11.54% x 16.9M = $1,950,000. This much is
explained fairly well by B/F.
But supposing the pattern has not really changed and IBNR is still 10% of
premium. The additional 200,000 of IBNR (1.5M-1.3M) is truly due to loss ratio
deterioration in the last quarter of the second year. That would mean in the
third year, you would still expect 10% IBNR, or 1.69M, plus four quarters of
deterioration (4 x $200,000) per some base. If you take the difference
3,039,000 - 1,690,000 that equals 1,349,000, the deterioration.
1,349,000/800,000=1.686 which looks like the amount of growth since the first
year (1.3)^2 = 1.69. I'm not sure I understand why two years of growth are
applied if the 200K pops up in the last quarter of the second year.
Anyone?
Annmarie_Schuster@CUUSA.com ("Schuster, Annmarie") on 07/15/98 11:14:00 AM
To: studygroup7@lists.casact.org @ INTERNET
cc: (bcc: Gwendolyn L. Anderson)
Subject: Bornhuetter/Ferguson The Actuary and IBNR
On the bottom of page 184, can anyone explain how B/F arrived at the
$3,039,000 figure for the 1971 IBNR reserve?
Thanks,
Annie