Bornhuetter–Ferguson method

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

Contents

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.

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Loss development factors or LDFs are used in insurance pricing and reserving to adjust claims to their projected ultimate level. Insurance claims, especially in long-tailed lines such as liability insurance, are often not paid out immediately. Claims adjusters set initial case reserves for claims; however, it is often impossible to predict immediately what the final amount of an insurance claim will be, due to uncertainty around defense costs, settlement amounts, and trial outcomes. Loss development factors are used by actuaries, underwriters, and other insurance professionals to "develop" claim amounts to their estimated final value. Ultimate loss amounts are necessary for determining an insurance company's carried reserves. They are also useful for determining adequate insurance premiums, when loss experience is used as a rating factor

References

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