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📐 '''Reserve triangle''' is a tabular data structure used by actuaries and insurance financial professionals to organize and analyze the development of [[Definition:Loss reserve | loss reserves]] over time, tracking how [[Definition:Incurred loss | incurred]] or [[Definition:Paid loss | paid]] losses for a given [[Definition:Accident year | accident year]] (or [[Definition:Underwriting year | underwriting year]]) evolve as more information becomes available. Each row of the triangle represents a cohort of claims originating in a specific period, while each column represents a successive development period — typically measured in months or years after the origin date. When the data is laid out, the diagonal edge of the table forms the characteristic triangular shape that gives the tool its name, with the most recent origin periods having the least development data and the oldest periods approaching their ultimate settled values.

⚙️ Actuaries populate reserve triangles with either cumulative paid losses, cumulative incurred losses, or reported claim counts, then apply projection techniques to estimate how each cohort will develop to its [[Definition:Ultimate loss | ultimate]] value. The [[Definition:Chain-ladder method | chain-ladder method]] is the most widely used approach: it calculates [[Definition:Loss development factor (LDF) | loss development factors]] from column to column, averages them across origin years, and applies the resulting pattern to project incomplete cohorts to completion. More sophisticated variations — such as the [[Definition:Bornhuetter-Ferguson method | Bornhuetter-Ferguson method]], the [[Definition:Cape Cod method | Cape Cod method]], and [[Definition:Stochastic reserving | stochastic reserving]] techniques — also rely on triangle data but introduce additional assumptions or statistical frameworks to improve accuracy, especially when historical patterns may not be stable. Reserve triangles are a universal tool across jurisdictions, used under [[Definition:US GAAP | US GAAP]], [[Definition:IFRS 17 | IFRS 17]], and the regulatory reporting requirements of bodies such as the [[Definition:National Association of Insurance Commissioners (NAIC) | NAIC]], the [[Definition:Prudential Regulation Authority (PRA) | PRA]], and supervisory authorities across Asia.

📊 Beyond their core role in [[Definition:Reserving | reserving]], reserve triangles serve as a diagnostic instrument. By examining how development patterns shift across origin years, actuaries can identify emerging trends — accelerating claim settlements, deteriorating [[Definition:Loss ratio (L/R) | loss ratios]], or the onset of [[Definition:Social inflation | social inflation]] in liability lines. A triangle that shows consistently adverse development in recent diagonals may signal a [[Definition:Deficient reserve | deficient reserve]], prompting management to strengthen its position. [[Definition:Reinsurer | Reinsurers]] and rating agencies routinely request reserve triangle data during due diligence and [[Definition:Financial strength rating | rating]] reviews, treating the quality and consistency of an insurer's triangles as a barometer of its actuarial discipline. For any professional working in insurance finance, reading and interpreting reserve triangles is a foundational skill.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Loss reserve]]
* [[Definition:Chain-ladder method]]
* [[Definition:Loss development factor (LDF)]]
* [[Definition:Bornhuetter-Ferguson method]]
* [[Definition:Incurred but not reported (IBNR)]]
* [[Definition:Deficient reserve]]
{{Div col end}}

Definition:Reserve triangle - Revision history

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