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: Allstate Ins Co 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 | 325,322 | 325,322 | 325,322 | 325,322 |
| AY 2 | 276,864 | 273,873 | 276,831 | 273,873 |
| AY 3 | 268,961 | 256,788 | 268,410 | 256,788 |
| AY 4 | 258,402 | 239,195 | 256,975 | 239,195 |
| AY 5 | 180,151 | 159,496 | 177,783 | 159,496 |
| AY 6 | 104,286 | 87,215 | 101,492 | 87,215 |
| AY 7 | 119,003 | 91,077 | 112,450 | 91,077 |
| AY 8 | 132,157 | 87,311 | 116,939 | 87,311 |
| AY 9 | 90,948 | 44,916 | 67,649 | 44,916 |
| AY 10 | 3,110 | 691 | 1,228 | 691 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 2,991 | 0 | 2,958 | 0 |
| AY 3 | 12,173 | 0 | 11,622 | 0 |
| AY 4 | 19,207 | 0 | 17,780 | 0 |
| AY 5 | 20,655 | 0 | 18,287 | 0 |
| AY 6 | 17,071 | 0 | 14,277 | 0 |
| AY 7 | 27,926 | 0 | 21,373 | 0 |
| AY 8 | 44,846 | 0 | 29,628 | 0 |
| AY 9 | 46,032 | 0 | 22,733 | 0 |
| AY 10 | 2,419 | 0 | 537 | 0 |
| Total | 193,320 | 0 | 139,195 | 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.