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

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