Bornhuetter-Ferguson method
The Bornhuetter-Ferguson method is a prominent[1][2][3][4][5][6] loss reserving technique.
Background
The Bornhuetter-Ferguson method was introduced in the 1972 paper "The Actuary and IBNR," co-authored by Ron Bornhuetter and Ron Ferguson.[4][5][7][8]
Like other loss reserving techniques, the Bornhuetter-Ferguson method aims to estimate incurred but not reported insurance claim amounts. It is primarily used in the property and casualty[5][9] and health insurance[2] fields.
Generally considered a blend of the chain-ladder and expected claims loss reserving methods,[2][8][10] the Bornhuetter-Ferguson method uses both reported or paid losses as well as an a priori expected loss ratio to arrive at an ultimate loss estimate.[2][9] Simply, reported (or paid) losses are added to a priori expected losses multiplied by an estimated percent unreported. The estimated percent unreported (or unpaid) is established by observing historical claims experience.[2]
The Bornhuetter-Ferguson method can be used with either reported or paid losses.[2][5]
Methodology
There are two algebraically equivalent approaches to calculating the Bornhuetter-Ferguson ultimate loss.
In the first approach, undeveloped reported (or paid) losses are added directly to expected losses (based on an a priori loss ratio) multiplied by an estimated percent unreported.
[math]\displaystyle{ BF = L + ELR * Exposure * (1 - w) }[/math][2][5][10]
In the second approach, reported (or paid) losses are first developed to ultimate using a chain-ladder approach and applying a loss development factor (LDF). Next, the chain-ladder ultimate is multiplied by an estimated percent reported. Finally, expected losses multiplied by an estimated percent unreported are added (as in the first approach).
[math]\displaystyle{ BF = L * LDF * w + ELR * Exposure * (1 - w) }[/math][2][5]
The estimated percent reported is the reciprocal of the loss development factor.[2][5]
Incurred but not reported claims can then be determined by subtracting reported losses from the Bornhuetter-Ferguson ultimate loss estimate.
See also
References
- ↑ https://www.scor.com/en/sgrc/risk-management/reserving/item/2099-measuring-the-variability-of-chain-ladder-reserve-estimates.html?lout=sgrc
- ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 "Archived copy". Archived from the original on 2014-03-27. https://web.archive.org/web/20140327110448/http://www.soa.org/files/pd/health/hspring07-005bk.pdf. Retrieved 2016-03-13.
- ↑ http://us.milliman.com/uploadedFiles/insight/pc-published/pdfs/fresh-look-at-actuarial.pdf
- ↑ 4.0 4.1 http://www.variancejournal.org/issues/02-01/85.pdf
- ↑ 5.0 5.1 5.2 5.3 5.4 5.5 5.6 https://www.casact.org/library/studynotes/Friedland_estimating.pdf
- ↑ http://www.casact.org/members/index.cfm?fa=viewArticle&articleID=709
- ↑ https://www.casact.org/pubs/proceed/proceed72/72181.pdf
- ↑ 8.0 8.1 http://www.investopedia.com/terms/b/bornhuetterferguson-technique.asp
- ↑ 9.0 9.1 https://www.casact.org/library/studynotes/Werner_Modlin_Ratemaking.pdf
- ↑ 10.0 10.1 http://www.variancejournal.org/issues/01-02/292.pdf
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