Bornhuetter–Ferguson method

The Bornhuetter–Ferguson method is a loss reserving technique in insurance.[1][2][3][4][5][6]

Background

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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

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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.

 [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).

 [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.

References

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  1. ^ "Risk Knowledge | SCOR".
  2. ^ a b c d e f g h i "Archived copy" (PDF). Archived from the original (PDF) on 2014-03-27. Retrieved 2016-03-13.{{cite web}}: CS1 maint: archived copy as title (link)
  3. ^ "Archived copy" (PDF). Archived from the original (PDF) on 2018-01-01. Retrieved 2016-02-28.{{cite web}}: CS1 maint: archived copy as title (link)
  4. ^ a b "Archived copy" (PDF). Archived from the original (PDF) on 2016-03-03. Retrieved 2016-03-07.{{cite web}}: CS1 maint: archived copy as title (link)
  5. ^ a b c d e f g Jacqueline Friedland (30 July 2010). "Estimating Unpaid Claims Using Basic Techniques" (PDF). casact.org. Retrieved 19 August 2023.
  6. ^ "Casualty Actuarial Society | Ronald Bornhuetter – in Memoriam". Archived from the original on 2016-03-07. Retrieved 2016-02-28.
  7. ^ The actuary and ibnr casact.org
  8. ^ a b "Bornhuetter-Ferguson Technique: Overview, Calculations". Investopedia. Retrieved 19 August 2023.
  9. ^ a b Basic Ratemaking casact.org
  10. ^ a b "Archived copy" (PDF). Archived from the original (PDF) on 2017-12-15. Retrieved 2016-03-07.{{cite web}}: CS1 maint: archived copy as title (link)