Taylor & Ashe (1983) — General Liability (classic textbook triangle)
The most widely cited loss-development triangle in the reserving literature (used by Mack to derive the chain-ladder standard error formula). Only the upper (observed) triangle is known — there is no 'actual outcome' lower triangle, unlike the CAS Loss Reserve Database entries.
Source: Taylor, G.C. & Ashe, F.R. (1983); also used in Mack (1993) as the 'GenIns' triangle. Taylor, G.C. and Ashe, F.R. (1983). Second Moments of Estimates of Outstanding Claims. Journal of Econometrics 23. Also reproduced in Mack, T. (1993), ASTIN Bulletin 23(2), as the 'GenIns' example triangle.
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Paid loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1977 | 357,848 | 1,124,788 | 1,735,330 | 2,218,270 | 2,745,596 | 3,319,994 | 3,466,336 | 3,606,286 | 3,833,515 | 3,901,463 |
| 1978 | 352,118 | 1,236,139 | 2,170,033 | 3,353,322 | 3,799,067 | 4,120,063 | 4,647,867 | 4,914,039 | 5,339,085 | — |
| 1979 | 290,507 | 1,292,306 | 2,218,525 | 3,235,179 | 3,985,995 | 4,132,918 | 4,628,910 | 4,909,315 | — | — |
| 1980 | 310,608 | 1,418,858 | 2,195,047 | 3,757,447 | 4,029,929 | 4,381,982 | 4,588,268 | — | — | — |
| 1981 | 443,160 | 1,136,350 | 2,128,333 | 2,897,821 | 3,402,672 | 3,873,311 | — | — | — | — |
| 1982 | 396,132 | 1,333,217 | 2,180,715 | 2,985,752 | 3,691,712 | — | — | — | — | — |
| 1983 | 440,832 | 1,288,463 | 2,419,861 | 3,483,130 | — | — | — | — | — | — |
| 1984 | 359,480 | 1,421,128 | 2,864,498 | — | — | — | — | — | — | — |
| 1985 | 376,686 | 1,363,294 | — | — | — | — | — | — | — | — |
| 1986 | 344,014 | — | — | — | — | — | — | — | — | — |
Incurred loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1977 | 357,848 | 1,124,788 | 1,735,330 | 2,218,270 | 2,745,596 | 3,319,994 | 3,466,336 | 3,606,286 | 3,833,515 | 3,901,463 |
| 1978 | 352,118 | 1,236,139 | 2,170,033 | 3,353,322 | 3,799,067 | 4,120,063 | 4,647,867 | 4,914,039 | 5,339,085 | — |
| 1979 | 290,507 | 1,292,306 | 2,218,525 | 3,235,179 | 3,985,995 | 4,132,918 | 4,628,910 | 4,909,315 | — | — |
| 1980 | 310,608 | 1,418,858 | 2,195,047 | 3,757,447 | 4,029,929 | 4,381,982 | 4,588,268 | — | — | — |
| 1981 | 443,160 | 1,136,350 | 2,128,333 | 2,897,821 | 3,402,672 | 3,873,311 | — | — | — | — |
| 1982 | 396,132 | 1,333,217 | 2,180,715 | 2,985,752 | 3,691,712 | — | — | — | — | — |
| 1983 | 440,832 | 1,288,463 | 2,419,861 | 3,483,130 | — | — | — | — | — | — |
| 1984 | 359,480 | 1,421,128 | 2,864,498 | — | — | — | — | — | — | — |
| 1985 | 376,686 | 1,363,294 | — | — | — | — | — | — | — | — |
| 1986 | 344,014 | — | — | — | — | — | — | — | — | — |