Actuarium

Quarterly rate & reserve review

Close the books on a real insurer's triangle: roll the reserves forward from the prior evaluation, test actual against expected emergence, re-estimate ultimate loss ratios and produce a credibility-weighted rate indication — then hand the decision to the Decision Studio.

Quarterly rate & reserve review

A period-end reserve roll-forward and rate indication on a real CAS Loss Reserve Database triangle. The database is annual (year-end evaluations); a live quarterly cycle applies the same roll-forward logic at each quarter-end instead.

Prior evaluation compared below: 1996.

Reserves — as of 1997 vs. prior (1996)

AYAgeReportedCL ultimateBF ultimateSelectedIBNRΔ ultimate vs priorHindsight ultimate
1988 (CL)10886,334886,334886,334886,3340707886,334
1989 (CL)9982,148982,932982,769982,9327841,765982,763
1990 (CL)81,075,5371,079,1021,078,4031,079,1023,5652,0741,079,195
1991 (CL)71,138,3751,146,6971,145,5511,146,6978,322-1,6981,146,042
1992 (CL)61,226,6501,246,1461,244,4841,246,14619,496-4,5301,244,693
1993 (CL)51,324,7321,375,0731,371,5871,375,07350,341-15,0071,377,723
1994 (CL)41,320,1301,440,5281,434,7431,440,528120,398-35,3851,433,285
1995 (CL)31,185,3001,430,7551,426,3791,430,755245,455-40,1481,435,077
1996 (BF)2966,1621,455,9081,441,7941,441,794475,632-60,2411,413,844
1997 (BF)1542,0211,568,8041,474,7241,474,724932,7031,474,7241,394,268
Total10,647,38912,504,0841,856,695
Total unpaid / IBNR
$1,856,695k
Mack std. error (total)
$149,116k
Mack CV
7.6%

Rate indication

AYUltimate LRTrend yearsTrended LR
198880.1%10.0107.7%
198982.2%9.0107.3%
199081.1%8.0102.7%
199175.6%7.092.9%
199271.2%6.085.1%
199370.0%5.081.2%
199468.4%4.077.0%
199566.3%3.072.5%
199666.4%2.070.5%
199767.4%1.069.5%
3-yr weighted trended LR
76.8%
Indicated: 9.7%
5-yr weighted trended LR
80.9%
Indicated: 15.5%
Credibility Z (premium rule)
1.00
Complement: 14.0%
Credibility-weighted indication (3yr)
9.7%
Δ=ZΔ+(1Z)Δcomplement\Delta^{*}=Z\Delta + (1-Z)\Delta_{complement}

Assumptions & limitations
  • The CAS Loss Reserve Database records annual (year-end) diagonals only; each 'quarterly' evaluation here re-runs the same year-end roll-forward logic, standing in for what a quarterly cycle would repeat four times a year.
  • Selected ultimate uses chain-ladder for accident years at least 3 years mature and Bornhuetter–Ferguson (a-priori = prior-evaluation weighted ultimate LR) for younger years.
  • Full credibility is assumed at $250,000,000 of premium (a stated proxy for the classical 1,082-claim standard, since Schedule P carries no claim counts).
  • The complement of credibility is the prior evaluation's own 3-year indicated change, trended forward one year; it is 0 when no prior evaluation exists.
  • Tail development beyond age 120 months is not observed in Schedule P and is assumed to be 1.0.
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