Friedland09.BornFerg

Reading: Friedland, J.F., Estimating Unpaid Claims Using Basic Techniques, Casualty Actuarial Society, Third Version, July 2010. The Appendices are excluded.

Chapter 9: Bornhuetter-Ferguson Method

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• fact A...
• fact B...

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #17)	ultimate: - reported B-F	ultimate: - reported B-F	combining data: - argument against
E (2019.Spring #19)	Friedland07.Development	ultimate: - reported B-F (tort reform)
E (2018.Spring #17)
E (2018.Spring #19)
E (2017.Spring #18)	Friedland08.ExpectedClms	unpaid & IBNR: - reported B-F
E (2016.Fall #21)	IBNR: - B-F method	ECR assumption: - assess reasonableness	alternate method: - recommend & justify
E (2016.Spring #16)	Friedland08.ExpectedClms	Friedland07.Development	ultimate: - paid B-F
E (2015.Fall #18)	ultimate: - reported B-F	CDFs < 1.0: - does B-F still work?
E (2015.Spring #19)	ultimate: - reported B-F	selected ultimates: - discuss appropriateness	ultimate: - Benktander	unpaid: - explain Benktander iterations
E (2014.Fall #18)	IBNR: - Benktander	credibility weighting: - explain Benktander
E (2014.Spring #14)	ultimate: - reported B-F	rptd B-F vs rptd dvlpt: - situations where equal	rptd B-F vs rptd dvlpt: - situations B-F is better
E (2013.Fall #17)	unpaid: - Benktander	unpaid: - Benktander 1000 iterations
E (2013.Spring #4)	ultimate: - reported B-F
E (2013.Spring #18)	key assumption: - B-F method	credibility-weighting: - explain for B-F	credibility-weighting: - violation of assumption	(d) paid vs rptd B-F for rising LRs (e) B-F vs Cape Cod

In Plain English!

Example A: Intro to BF Method

The following information is as of Dec 31, 2023. Calculate the ultimate for AY 2023 using the reported Bornhuetter-Ferguson method.

EP	1,000
ECR	65%
reported claims12	375
reported CDF12→ult	1.4

First, note how easy it is to calculate the ultimate using the reported development method:

• Ult_r-Dev   =   375 x 2.0   =   750

And the ultimate for the ECR method is equally easy:

• Ult_ECR   =   65% x 1,000   =   650

The reported BF method is just a weighted average of these where the weight, z, given to the reported development method is:

z   =   %reported   =   1 – 1/CDF

So,

• z   =   1 – 1/CDF_12→ult   =   1 – 1/1.4   =   0.286

and therefore,

• Ult_r-BF   =   [ 0.286 x 750 ] + [ (1 – 0.286) x 650 ]   =   679

Actually, there's a simpler but equivalent formula for the BF ultimate:

Ultr-BF   =   (reported claims) + %unreported x UltECR

The proof that these formulations of the BF method are equivalent is not likely to be asked on the exam but you can click the link if you'd like to see it. It's easy. Anyway, let's verify that this simpler formula gives the same result as above.

Ult_r-BF   =   (reported claims) + %unreported x Ult_ECR   =   375 + (1 – 1/CDF) x 650   =   375 + (1 – 1/1.4) x 650   =  

(There's also a paid version of BF and it works exactly like the reported version.)