Claims development
Development triangles and a first look at the chain ladder.
The claims for a year keep growing long after the year ends: late reports arrive, reserves are revised, payments continue. A development triangle shows that growth, and lets an actuary estimate where it will end.
The triangle
Rows are accident years, the year the loss happened. Columns are development years: 0 is the accident year itself, 1 the year after, and so on. Each cell holds the amount paid so far, cumulated. Because later years have had less time to develop, the known cells form a triangle.
| Accident year | Development year 0 | 1 | 2 |
|---|---|---|---|
| 2023 | 838,773.04 | 1,057,144.01 | 1,057,144.01 |
| 2024 | 1,790,894.10 | 2,090,776.40 | |
| 2025 | 1,938,137.31 |
Development factors
How much does a year's paid amount grow from one development year to the next? The age-to-age factor divides the later column by the earlier one, over the years that have both:
From development year 1 to 2 only 2023 is known, and it did not grow: , because Harbour Mutual settles most claims within a year of the loss.
The chain ladder
Multiplying the latest known cell by the factors still to come projects each year's ultimate cost. For 2025:
About €382,000 more is expected to be paid for 2025's losses: open claims still to be settled and claims not yet reported. That is the reserve the chain ladder suggests for 2025, on paid amounts alone.
Check your understanding
Answer every question, then check.