Bornhuetter-Ferguson Calculator

BF IBNR represents losses that have been incurred but not yet reported -- it's calculated as Expected Losses times Unreported Factor, an a priori estimate of what's still to come, not an adjustment based on what's already been reported. Reported Losses does feed into BF Ultimate Loss directly (it's added on top of BF IBNR), but it plays no role in the IBNR estimate itself.

A pure chain-ladder projection multiplies Reported Losses by the Development Factor to estimate ultimate losses, relying entirely on claims reported so far. BF instead only applies that full credibility to the already-reported portion, and uses an independent a priori Expected Loss Ratio estimate (not tied to what's been reported) for the remaining, not-yet-reported portion -- making BF less volatile than chain-ladder early in an accident year, when little has been reported and a chain-ladder projection would be unstable.

A Development Factor of 1.25 implies Unreported Factor of 0.2 (1 minus 1 divided by 1.25) -- meaning an estimated 20% of ultimate losses for this accident year have not yet been reported, and 80% (1 divided by 1.25) already have. Higher Development Factors imply a larger unreported share, since a higher factor means losses take longer to fully emerge.

Expected Loss Ratio is a pure a priori assumption you enter as an input. Implied Loss Ratio is calculated backward from the actual BF Ultimate Loss result (which blends in Reported Losses) divided by Earned Premium -- so it reflects both your a priori assumption AND the reported claims experience, and will diverge from Expected Loss Ratio whenever reported losses are running higher or lower than the a priori assumption implied they would be at this stage of development.