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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.

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Loaded: Allstate Ins Co Grp — Workers' Compensation (paid, CAS Loss Reserve DB)
Origin \ Dev12345678910
AY 1
AY 2
AY 3
AY 4
AY 5
AY 6
AY 7
AY 8
AY 9
AY 10

Premium by origin year & expected loss ratio

Ultimate comparison

Origin yearCL ultimateBF ultimateBenktander ultimateCape Cod ultimate
AY 1325,322325,322325,322325,322
AY 2276,864273,873276,831273,873
AY 3268,961256,788268,410256,788
AY 4258,402239,195256,975239,195
AY 5180,151159,496177,783159,496
AY 6104,28687,215101,49287,215
AY 7119,00391,077112,45091,077
AY 8132,15787,311116,93987,311
AY 990,94844,91667,64944,916
AY 103,1106911,228691

IBNR comparison

Origin yearCL IBNRBF IBNRBenktander IBNRCape Cod IBNR
AY 10000
AY 22,99102,9580
AY 312,173011,6220
AY 419,207017,7800
AY 520,655018,2870
AY 617,071014,2770
AY 727,926021,3730
AY 844,846029,6280
AY 946,032022,7330
AY 102,41905370
Total193,3200139,1950

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.
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