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📐 '''Loss development triangle''' is a tabular display used by [[Definition:Actuary | actuaries]] to organize and analyze how [[Definition:Incurred loss | incurred losses]] or [[Definition:Paid loss | paid losses]] for a set of [[Definition:Accident year | accident years]] (or [[Definition:Policy year | policy years]]) evolve as they mature over successive evaluation periods. The triangle gets its name from its characteristic shape: the oldest accident year has the most data points running across the columns, while the most recent year has only one — creating a triangular pattern. It is the primary analytical tool used in [[Definition:Reserving | loss reserving]] and serves as the foundation for calculating [[Definition:Loss development factor | loss development factors]].

🔍 Each row of the triangle represents a distinct origin period — most commonly an accident year — and each column represents a valuation point measured in months or years of maturity. The cells contain the cumulative [[Definition:Claim | claim]] amounts at each intersection of origin period and maturity. By reading across a single row, an analyst can observe how losses for that particular year progressed over time. By reading down a single column, one can compare the maturity profile across different origin years at the same development stage. Actuaries extract age-to-age factors from adjacent columns and use methods such as the [[Definition:Chain-ladder method | chain-ladder technique]], [[Definition:Bornhuetter-Ferguson method | Bornhuetter-Ferguson method]], or [[Definition:Cape Cod method | Cape Cod method]] to project the incomplete rows to their [[Definition:Ultimate loss | ultimate]] values. Triangles can be constructed on an incurred basis (reserves plus payments), a paid basis, or both, and the comparison between the two often reveals important insights about [[Definition:Case reserve | case reserving]] adequacy.

💡 Despite its apparent simplicity, the loss development triangle is one of the most scrutinized artifacts in insurance finance. [[Definition:Insurance regulation | Regulators]] require carriers to file [[Definition:Schedule P | Schedule P]] triangles in their [[Definition:Annual statement | annual statements]], giving external reviewers a window into how prior estimates have held up. Significant changes in the pattern — caused by shifts in [[Definition:Claims management | claims handling]] practices, [[Definition:Social inflation | social inflation]], changes in business mix, or one-time events — can distort the factors derived from a triangle and lead to materially different reserve estimates. [[Definition:Reinsurance | Reinsurers]], [[Definition:Rating agency | rating agencies]], and investors all rely on triangle analysis when evaluating an insurer's financial condition. For [[Definition:Insurtech | insurtech]] platforms building automated reserving tools, the ability to ingest, validate, and model triangle data accurately is a foundational technical requirement.

'''Related concepts'''
{{Div col|colwidth=20em}}
* [[Definition:Loss development factor]]
* [[Definition:Loss development]]
* [[Definition:Chain-ladder method]]
* [[Definition:Reserving]]
* [[Definition:Schedule P]]
* [[Definition:Bornhuetter-Ferguson method]]
{{Div col end}}

Definition:Loss development triangle - Revision history

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