Bornhuetter–Ferguson / Benktander / Cape Cod
Blend a-priori expected losses with emerged experience via BF, its iterated Benktander form, and the data-driven Cape Cod method, side by side with chain-ladder.
Loaded: Taylor & Ashe (1983) — General Liability (classic textbook triangle) (paid, CAS Loss Reserve DB)
| Origin \ Dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
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| AY 10 |
Premium by origin year & expected loss ratio
Ultimate comparison
| Origin year | CL ultimate | BF ultimate | Benktander ultimate | Cape Cod ultimate |
|---|---|---|---|---|
| AY 1 | 3,901,463 | 3,901,463 | 3,901,463 | 3,901,463 |
| AY 2 | 5,433,719 | 5,339,085 | 5,432,071 | 5,339,085 |
| AY 3 | 5,378,826 | 4,909,315 | 5,337,843 | 4,909,315 |
| AY 4 | 5,297,906 | 4,588,268 | 5,202,852 | 4,588,268 |
| AY 5 | 4,858,200 | 3,873,311 | 4,658,536 | 3,873,311 |
| AY 6 | 5,111,171 | 3,691,712 | 4,716,963 | 3,691,712 |
| AY 7 | 5,660,771 | 3,483,130 | 4,823,055 | 3,483,130 |
| AY 8 | 6,784,799 | 2,864,498 | 4,519,624 | 2,864,498 |
| AY 9 | 5,642,266 | 1,363,294 | 2,397,187 | 1,363,294 |
| AY 10 | 4,969,825 | 344,014 | 664,215 | 344,014 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 94,634 | 0 | 92,986 | 0 |
| AY 3 | 469,511 | 0 | 428,528 | 0 |
| AY 4 | 709,638 | 0 | 614,584 | 0 |
| AY 5 | 984,889 | 0 | 785,225 | 0 |
| AY 6 | 1,419,459 | 0 | 1,025,251 | 0 |
| AY 7 | 2,177,641 | 0 | 1,339,925 | 0 |
| AY 8 | 3,920,301 | 0 | 1,655,126 | 0 |
| AY 9 | 4,278,972 | 0 | 1,033,893 | 0 |
| AY 10 | 4,625,811 | 0 | 320,201 | 0 |
| Total | 18,680,856 | 0 | 7,295,718 | 0 |
IBNR by method
Assumptions & limitations
- Premium is on-level (rate and mix adjusted) so that a single expected loss ratio is meaningful across origin years.
- The a-priori expected loss ratio is a credible, independent estimate (e.g., pricing plan or industry benchmark) — not derived from the same data being reserved.
- Cape Cod pools all origin years to estimate a single ELR from the data; it will differ from a manually chosen BF a-priori.