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: Erie Ins Exchange Grp — Workers' Compensation (paid, CAS Loss Reserve DB)
| Origin \ Dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
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Premium by origin year & expected loss ratio
Ultimate comparison
| Origin year | CL ultimate | BF ultimate | Benktander ultimate | Cape Cod ultimate |
|---|---|---|---|---|
| AY 1 | 26,113 | 26,113 | 26,113 | 26,113 |
| AY 2 | 35,168 | 34,988 | 35,168 | 34,988 |
| AY 3 | 41,604 | 41,015 | 41,596 | 41,015 |
| AY 4 | 52,338 | 50,439 | 52,269 | 50,439 |
| AY 5 | 67,843 | 63,051 | 67,505 | 63,051 |
| AY 6 | 75,840 | 67,202 | 74,856 | 67,202 |
| AY 7 | 75,539 | 61,579 | 72,959 | 61,579 |
| AY 8 | 78,715 | 55,908 | 72,107 | 55,908 |
| AY 9 | 76,878 | 42,087 | 61,133 | 42,087 |
| AY 10 | 83,119 | 22,408 | 38,775 | 22,408 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 180 | 0 | 180 | 0 |
| AY 3 | 589 | 0 | 581 | 0 |
| AY 4 | 1,899 | 0 | 1,830 | 0 |
| AY 5 | 4,792 | 0 | 4,454 | 0 |
| AY 6 | 8,638 | 0 | 7,654 | 0 |
| AY 7 | 13,960 | 0 | 11,380 | 0 |
| AY 8 | 22,807 | 0 | 16,199 | 0 |
| AY 9 | 34,791 | 0 | 19,046 | 0 |
| AY 10 | 60,711 | 0 | 16,367 | 0 |
| Total | 148,368 | 0 | 77,691 | 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.