Bornhuetter–Ferguson method

The Bornhuetter-Ferguson method is a prominent 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.

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 and health insurance fields.

Generally considered a blend of the chain-ladder and expected claims loss reserving methods, 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. 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.

The Bornhuetter-Ferguson method can be used with either reported or paid losses.

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.

$BF=L+ELR*Exposure*(1-w)$

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).

$BF=L*LDF*w+ELR*Exposure*(1-w)$

The estimated percent reported is the reciprocal of the loss development factor.

Incurred but not reported claims can then be determined by subtracting reported losses from the Bornhuetter-Ferguson ultimate loss estimate.

See also

• Loss reserving