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piemedia
03-17-2012, 12:02 PM
if ELR= 75%, % Unreported: 0.652, Rpt loss: 700, EP=2600

By BF method, Ult. Loss = 700 + (1950*0.652) = 1971, IBNR= 1271

If L/R deteriorating to 95%, by BF method, Ult loss = 700 +(2600*.95*.652)=2310, IBNR=1610,,,,, so, IBNR is increased from 1271 to 1610,,,,,

so, if L/R deteriorating, BF method provided overstated IBNR,,, right?
But, answer is IBNR is understated,,,,

Why is that? What part am I missing? Thank you for your help....

Vorian Atreides
03-17-2012, 01:06 PM
if ELR= 75%, % Unreported: 0.652, Rpt loss: 700, EP=2600

By BF method, Ult. Loss = 700 + (1950*0.652) = 1971, IBNR= 1271

If L/R deteriorating to 95%, by BF method, Ult loss = 700 +(2600*.95*.652)=2310, IBNR=1610,,,,, so, IBNR is increased from 1271 to 1610,,,,,

so, if L/R deteriorating, BF method provided overstated IBNR,,, right?
But, answer is IBNR is understated,,,,

Why is that? What part am I missing? Thank you for your help....
In the bolded, you made a change to the ELR and show that the IBNR should be 1610.

What the text is saying is that if you made no changes to the ELR, the resulting IBNR will be understating what you really need for IBNR.

jesusislord
03-17-2012, 05:32 PM
this is a weakness of the BF method. it lacks responsiveness to the actual claims experience. in real life, the actuary would adjust the loss rate/ claim ratio. however, if the loss rate is not adjusted, the ibnr would be understated.

piemedia
03-18-2012, 08:14 PM
In the bolded, you made a change to the ELR and show that the IBNR should be 1610.

What the text is saying is that if you made no changes to the ELR, the resulting IBNR will be understating what you really need for IBNR.

Ok, then,,, if ELR= 70% is consistent, so current ult L/R is 75.8% (=1971/2600), but deteriorating ult L/R is 90%,,, so then ult loss will be 2340(=2600* 90%),,, rpt loss is still 700, and IBNR is 1640.... So IBNR is increased from 1271,,,, Right? So, the BF method shows IBNR overstated by deteriorating ult L/R ,,,, correct?

Vorian Atreides
03-19-2012, 09:51 AM
#1. Start with the assumption that you had perfect knowledge; and it was that the ult LR would be 90%. Then the required IBNR (given the other information you provided in the OP are also perfect) would be \$1,610.

#2. In reality, you don't have perfect knowledge. So, if historically, 75% was a reasonable assumption for the ult LR (per the OP), you would end up with the estimate of \$1,271 by the BF method. That is, the BF method is not responsive to a book with a deteriorating losses. Furthermore, this estimate will understate the true IBNR requirement. Put another way, you should have \$1,610 IBNR, but you're only showing \$1,271. You're going to be short by \$339.

magellan
03-28-2012, 02:26 PM
There are two LRs we are talking about. One is ELR or expected loss ratio (a known quantity) and then, the other is actual loss ratio (let’s call it ALR, an unknown quantity). Correspondingly, we have:

(1) BF IBNR = ELR * Premium * % Unreported
(2) Actual IBNR = ALR * Premium * % Unreported

If LR worsens from the expectation (i.e. known ELR), then ALR = (ELR + alpha), for some positive % alpha.

This gives, from (2),
(3) Actual IBNR = (ELR + alpha)*Premium*%Unreported = (ELR * Premium * % Unreported) + (alpha * Premium * % Unreported) = BF IBNR + a positive quantity

This gives,
Actual IBNR > BF IBNR. i.e., BF IBNR underestimates when LR deteriorates.

Similarly, if actual LR improves from the expectation i.e. ALR = ELR – alpha, then (a) will give us: Actual IBNR = BF IBNR – a positive quantity
This will give,
Actual IBNR < BF IBNR. i.e., BF IBNR overestimates when LR improves.

Vorian Atreides
03-28-2012, 03:37 PM
Oh, sure! Bring that fancy math in here will all of those greek letters and what not!!

;-)