Bornhuetter-Ferguson method
A reserving method that estimates the unreported part of an accident year from an expected loss ratio rather than from reported claims, which makes it more stable on immature years.
The Bornhuetter-Ferguson method (Ronald Bornhuetter and Ronald Ferguson, 1972), BF for short, sets an accident year's IBNR as earned premium, times an a priori loss ratio, times the share of the cost still to be reported, 1 − 1/CDF, where CDF is the chain ladder cumulative factor at the year's age. The ultimate is reported incurred plus that IBNR: what is already reported counts once and is not multiplied by the factor. It reads as a credibility blend. The BF ultimate weights the chain ladder ultimate by 1/CDF and the a priori ultimate by 1 − 1/CDF, so a young year leans almost entirely on the prior and a mature year converges on chain ladder. Everything rests on that a priori loss ratio, and an optimistic prior flows straight into the reserve, with no correction from observed experience until the year has matured. The method borrows the chain ladder development pattern and replaces only the projection, which makes it the natural companion on the two or three youngest years, and the first check on an IBNR that looks too high or too low. Its neighbors settle the prior differently: Cape Cod estimates it from the triangle itself, Benktander runs BF a second time.
Example, using the triangle from the chain ladder entry: accident year 2025 at 12 months, in thousands of euros: reported incurred 1,300, cumulative factor 1.7371, earned premium 3,000, a priori loss ratio 70%. Share still to be reported: 1 − 1/1.7371 = 0.4243. IBNR: 3,000 × 0.70 × 0.4243 = 891; ultimate: 1,300 + 891 = 2,191, against 2,258 by chain ladder. Had a 300 claim been reported in the first year (incurred 1,600), chain ladder would take the ultimate to 1,600 × 1.7371 = 2,779, 521 more for a 300 claim; Bornhuetter-Ferguson would take it to 1,600 + 891 = 2,491, 300 more, the claim and nothing else.
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