RE: Bornhuetter/Ferguson The Actuary and IBNR

Hill, Robert ( (no email) )
Thu, 16 Jul 1998 08:19:52 -0700

I could tell you...
But then I'd have to kill you.
Okay, okay, you can get his answer by assuming that the real IBNR is 10%
plus deterioration in the third to fourth report for all years that have not
observed this level of maturity. The observed emergence in 1970 was from
what I will call accident year 1967 from 36 to 48 months. Accident year 1968
additional development will be "observed" during 1971. So we need the
additional amount for years 1969, 1970, and 1971 (the years which have yet
to develop from third to fourth report).
Take the $200 from 1967, increase it by 1.3 exposure growth raised to the
correct power.
200 x 1.3 ^2 = 338
200 x 1.3 ^ 3 = 439.4
200 x 1.3 ^ 4 = 571.2

IBNR = (10% of 16,900) + 338 + 439.4 + 571.2 = 3,039

Either that, or it just cannot be done; I'm not sure.

-----Original Message-----
From: Gwendolyn L. Anderson [SMTP:Gwendolyn_L._Anderson@ffic.com]
Sent: Wednesday, July 15, 1998 9:30 AM
To: Schuster Annmarie
Cc: studygroup7
Subject: Re: Bornhuetter/Ferguson The Actuary and IBNR

It's not really obvious. Let me tell you how much of it I
understand and then
maybe someone else can pick it up from there.

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