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A priori loss ratio

Loss ratio predicted before observing claims, derived from pricing or market analysis, used as the anchor in the Bornhuetter-Ferguson method.

Definition

Bornhuetter and Ferguson, 1972, “The Actuary and IBNR”, Proceedings of the Casualty Actuarial Society: the method that bears their names blends observed development with an expectation set in advance. That expectation is the a priori loss ratio (expected loss ratio, ELR), an estimate of an accident year's loss ratio before its claims have developed enough to be statistically reliable. It comes from the pricing plan (pure premium over expected earned premium), from market analyses or from a credibility-weighted average of prior years. For recent accident years, where data is sparse, it serves as the expert prediction, and the reliability of BF reserves depends directly on it. Too optimistic, and it produces systematic under-reserving; too conservative, over-reserving. Its annual revision is one of the actuary's major judgment calls.

Its 4 cross-references, woven across the glossary's 18 categories
A priori loss ratio: Actuarial science glossary illustration, AlgoPolis
Example

Accident year 2024, a priori LR = 68% (from 2024 pricing plan). After 12 months of development, observed LR = 52%. BF weights the two according to % developed (30%) → a priori still dominates.

Read next
Actuarial scienceBornhuetter-Ferguson methodA reserving method that estimates the unreported part of an accident year from an expected loss ratio rather than from reported claims, which makes it more stable on immature years.Read the entry →Actuarial scienceChain ladderReserving method that projects each accident year to its ultimate cost by applying the development factors observed on older accident years.Read the entry →Actuarial scienceCape Cod methodA variant of Bornhuetter-Ferguson that does not take the a priori loss ratio from expert judgment but computes it from the triangle itself, weighted by already developed exposure.Read the entry →
Put it to work
QuizEstimating what a year of claims will costAcademy questions on this concept, each one marked and explained.Test yourself →
Related terms
Also known as

a priori loss ratio, expected loss ratio, ELR, initial expected loss ratio

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