Loss triangle

Category: Actuarial fundamentals · Reviewed by Jake Leat, Associate Director · Last reviewed

Loss triangle

A loss triangle is a tabular representation of cumulative paid or incurred losses by origin period (rows) and development period (columns). It is the foundational data structure of general insurance reserving.

Structure

Rows are accident year, underwriting year or report year. Columns are development months (12, 24, 36 etc.). The triangle is “lower-left” — older origin years have more development columns filled; the most recent origin year has only the 12-month figure.

Example (cumulative paid £000s):

Acc Yr \ Dev	12	24	36	48	60
2020	2,100	4,200	5,000	5,300	5,400
2021	2,300	4,500	5,200	5,500
2022	2,400	4,700	5,400
2023	2,500	4,900
2024	2,600

Variants

• Paid loss triangle — cumulative paid.
• Incurred loss triangle — paid + case reserves.
• Reported claim count triangle — cumulative claim counts.
• Average cost per claim triangle.
• Closed claim triangle.

Uses

• Estimating ultimate losses (chain ladder, Bornhuetter-Ferguson, Cape Cod methods).
• Estimating IBNR.
• Stress testing the volatility of estimates (Mack method, Bootstrap, stochastic chain ladder).
• Calibrating reinsurance pricing models.

References

• Friedland, J. (CAS, 2010). Estimating Unpaid Claims Using Basic Techniques.
• IFoA. General insurance reserving practical guides.
• Mack, T. (1993). ASTIN Bulletin.

Cross-references

• Loss development
• Chain ladder method
• Bornhuetter Ferguson method
• Cape Cod method

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