A claim reported in 2022 might not close until 2026. A run-off triangle is how you line up those slow-maturing years side by side so a single development pattern jumps out.
Group claims by the period they belong to, the origin period, along the rows. Accident year is the most common choice, but you can pick from several bases. Report year groups by when the claim was reported, standard for claims-made coverages such as U.S. medical malpractice and errors-and-omissions. Underwriting year groups by the year a policy was underwritten, how reinsurers usually organize their experience. Treaty year aligns claims to the reinsurance treaty that covers them. Policy year groups by policy inception.
Choose your interval too. Rows can span a full year or run monthly, quarterly, or semi-annual. Trade the credibility of the experience against the stability of development, or both.
Along the columns runs development age: how mature the experience is, measured in months since the origin period began.
Common mistakes
- Computing link factors on incremental data. Factors belong to cumulative triangles. Using the incremental $900 where cumulative $2,400 was needed gives a meaningless ratio.
- Cumulating the case outstanding triangle. Case outstanding is an ending balance at each valuation, not a running total. Summing it across a row double-counts open reserves and inflates the reported triangle.
- Dropping a late-reported claim into an early cell. The accident date sets the row, but the report date sets the first cell a claim can touch. Placing Claim B in the 2021 accident-year 12-month cell overstates that valuation.
Bottom line
- A run-off triangle arrays experience by origin period (rows) and development age (columns); each row matures left to right.
- Rows are usually accident years; columns are ages like 12, 24, 36 months; the latest diagonal is the most recent valuation.
- A diagonal is one calendar (valuation) date; moving down-right one cell is one more year of development.
- Build separate triangles for paid losses, reported (incurred) losses, closed and reported claim counts, and ALAE.
Exam shortcut
To get any age-to-age factor fast, find the two cumulative cells in the same row and divide right by left. If the factor is below 1.0 on a paid triangle, suspect recoveries or a data flip. When you build from a listing, let the accident date pick the row and the report date pick the first live cell.
The full lesson (about 2,915 words, 19 min read) adds 3 worked examples, all 8 common mistakes, a self-check, free in the app.
Learning objectives
- B6
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