# Bornhuetter-Ferguson Technique

## What Is the Bornhuetter-Ferguson Technique?

The Bornhuetter-Ferguson technique is a method for working out an estimate of an insurance organization's losses. The Bornhuetter-Ferguson technique, likewise called the Bornhuetter-Ferguson method, estimates incurred yet not yet reported (IBNR) losses for a policy year. This technique was made by two actuaries, Bornhuetter and Ferguson, and was first introduced in 1975.

## How the Bornhuetter-Ferguson Technique Works

Bornhuetter-Ferguson is one of the most widely utilized loss reserve valuation methods, second just to the chain-ladder method. It consolidates highlights of the chain ladder and expected loss ratio methods and allots loads for the percentage of losses paid and losses incurred. Dissimilar to the chain ladder method, which constructs a model in light of past experience, the Bornhuetter-Ferguson technique fabricates a model in view of the insurer's exposure to loss.

There are two [algebraically equivalent methods](/arithmetical method) for computing loss, as per the Bornhuetter-Ferguson technique. In the principal approach, undeveloped reported (or paid) losses are added straightforwardly to expected losses (in view of a priori loss ratio), duplicated by an estimated percent unreported.

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

In the second calculation method, reported (or paid) losses are first developed to ultimate utilizing a chain-ladder approach and applying a loss development factor (LDF). Next, the chain-ladder ultimate is increased by an estimated percent reported. At last, expected losses duplicated by an estimated percent unreported are added (as in the main approach).

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

The estimated percent reported is the reciprocal of the loss development factor. IBNR claims are then figured by deducting reported losses from the Bornhuetter-Ferguson ultimate loss estimate.

## Bornhuetter-Ferguson Technique versus Chain Ladder Method

The chain ladder method looks at the point over a period in time in which a claim is reported or paid. Insurers utilize this to "spending plan" for future losses, with the sum of each representing things to come losses rising to the IBNR. Claim estimates from past time spans are made concrete, in view of loss experience. This means that the actuary swaps past estimates with real claims.

The Bornhuetter-Ferguson technique estimates IBNR during a period of time by assessing the ultimate loss for certain risk exposures and afterward assessing the percent of this ultimate loss that was not reported at that point. Bornhuetter-Ferguson works out the estimated loss as the sum of reported loss plus IBNR, with IBNR calculated as the estimated ultimate loss increased by the percentage of loss that is unreported. Loss estimates use priori loss estimates.

Bornhuetter-Ferguson might be the most valuable in situations where genuine reported losses don't give a decent indicator of IBNR. This is reasonable when losses are low frequency yet high seriousness, a combination that makes it more hard to give accurate estimates. It is more straightforward for an insurer to foresee what will occur with high frequency, low seriousness claims.

## Highlights

• The Bornhuetter-Ferguson technique joins highlights of the chain ladder and expected loss ratio methods and relegates loads for the percentage of losses paid and losses incurred.
• This is one of the most well known methods for computing loss reserves, second just to the chain-ladder method.
• The technique might be when losses are low frequency however high seriousness.
• The Bornhuetter-Ferguson technique is a method of assessing incurred however not yet reported (IBNR) losses for insurers.