Category: Actuarial fundamentals · Reviewed by Mark Fox, Broker · Renewals · Last reviewed
Bornhuetter-Ferguson method
The Bornhuetter-Ferguson (BF) method is a reserving technique that blends a prior estimate of ultimate losses (typically from pricing or expected loss ratios) with the chain-ladder development pattern. It was introduced by Ronald Bornhuetter and Ronald Ferguson in 1972 to address chain-ladder instability on immature accident years.
Expected Ultimate = a priori estimate (often Premium × ELR).
f = cumulative development factor from current age to ultimate.
The term (1 − 1/f) is the proportion of losses still to emerge under the chain-ladder pattern.
Why use BF rather than chain ladder?
Immature years. When only a tiny fraction of losses has emerged (e.g. 5% at 12 months for liability), chain-ladder factors of 20+ massively amplify random noise in the diagonal. BF anchors the estimate to the priced expectation.
Sparse data. New lines or small portfolios benefit from the regularising effect of an external prior.
Bayesian flavour. BF can be motivated as a Bayesian credibility-weighted estimate.
Limitations
Result depends heavily on the chosen a priori ELR. Mature years should rely less on the prior.
BF blends the prior and the chain ladder linearly; in some situations a weighted average (Cape Cod) is preferable.
References
Bornhuetter, R.L. and Ferguson, R.E. (1972). The Actuary and IBNR. Proceedings of the Casualty Actuarial Society 59.
