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)1051,93951,93951,93951,939012751,939
1989 (CL)946,22946,34246,36246,342113-60646,483
1990 (CL)853,95654,95554,90954,955999-31454,857
1991 (CL)766,56669,21768,88769,2172,651-1,21068,965
1992 (CL)659,43763,78663,80863,7864,349-86663,406
1993 (CL)550,74257,58359,40857,5836,841-1,69357,917
1994 (CL)445,58057,07059,26257,07011,490-2,31655,255
1995 (CL)344,04566,81360,27266,81322,7688,92067,011
1996 (BF)231,47468,70952,29952,29920,8257,62468,225
1997 (BF)19,37250,43933,22733,22723,85533,22755,377
Total459,340553,23293,892
Total unpaid / IBNR
$93,892k
Mack std. error (total)
$7,017k
Mack CV
5.5%

Rate indication

AYUltimate LRTrend yearsTrended LR
198852.1%10.070.0%
198954.4%9.071.0%
199066.9%8.084.7%
199172.9%7.089.6%
199263.5%6.075.8%
199350.4%5.058.4%
199453.6%4.060.3%
199589.5%3.097.8%
199686.8%2.092.1%
199772.3%1.074.5%
3-yr weighted trended LR
69.0%
Indicated: -1.4%
5-yr weighted trended LR
74.4%
Indicated: 6.3%
Credibility Z (premium rule)
1.00
Complement: -8.4%
Credibility-weighted indication (3yr)
-1.4%
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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