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.

^[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.

See also

• Loss reserving

References