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)1026,11326,11326,11326,113013426,113
1989 (CL)934,98835,16835,12435,168180-11335,341
1990 (CL)841,01541,60441,42641,604589-44942,292
1991 (CL)750,43952,33851,74752,3381,899-21152,971
1992 (CL)663,05167,84366,31767,8434,792-1,23367,213
1993 (CL)567,20275,84074,27875,8408,638-2,01875,610
1994 (CL)461,57975,53975,64675,53913,960-2,10775,470
1995 (CL)355,90878,71580,71178,71522,807-3,33776,870
1996 (BF)242,08776,87880,06080,06037,973-3,63773,705
1997 (BF)122,40883,11976,35076,35053,94276,35074,731
Total464,790609,571144,781
Total unpaid / IBNR
$144,781k
Mack std. error (total)
$6,693k
Mack CV
4.5%

Rate indication

AYUltimate LRTrend yearsTrended LR
198853.6%10.072.1%
198963.6%9.082.9%
199068.5%8.086.8%
199169.3%7.085.3%
199270.1%6.083.7%
199358.3%5.067.6%
199447.4%4.053.3%
199543.9%3.048.0%
199645.6%2.048.3%
199749.4%1.050.8%
3-yr weighted trended LR
55.2%
Indicated: -21.1%
5-yr weighted trended LR
63.1%
Indicated: -9.9%
Credibility Z (premium rule)
1.00
Complement: -6.8%
Credibility-weighted indication (3yr)
-21.1%
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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