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)1075,65575,65575,65575,655054375,655
1989 (CL)970,84671,35871,18471,35851213571,001
1990 (CL)849,99450,79350,54150,79379911350,385
1991 (CL)741,97042,96942,67842,96999929142,887
1992 (CL)636,88438,36138,10938,3611,47798937,684
1993 (CL)520,81322,25723,16322,2571,4442,96227,752
1994 (CL)414,57016,74618,71316,7462,176-13321,102
1995 (CL)310,43913,65818,58913,6583,219-10,48014,678
1996 (BF)28,76816,21420,52620,52611,758-3,04413,544
1997 (BF)15,25821,67624,39624,39619,13824,39620,734
Total335,197376,72041,523
Total unpaid / IBNR
$41,523k
Mack std. error (total)
$7,393k
Mack CV
21.4%

Rate indication

AYUltimate LRTrend yearsTrended LR
198880.2%10.0107.7%
198977.4%9.0100.9%
199074.6%8.094.5%
199172.1%7.088.7%
199261.6%6.073.5%
199331.4%5.036.4%
199426.8%4.030.2%
199520.2%3.022.1%
199641.0%2.043.5%
199749.3%1.050.8%
3-yr weighted trended LR
29.6%
Indicated: -57.6%
5-yr weighted trended LR
49.0%
Indicated: -30.0%
Credibility Z (premium rule)
1.00
Complement: -40.2%
Credibility-weighted indication (3yr)
-57.6%
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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