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)106,815,6466,815,6466,815,6466,815,64606,8376,815,646
1989 (CL)97,712,0777,719,8217,718,2547,719,8217,7442,3657,721,911
1990 (CL)88,364,9558,396,6018,390,8938,396,60131,6461,7118,394,117
1991 (CL)78,215,8108,288,5458,281,1258,288,54572,735-2,2928,288,143
1992 (CL)68,876,8139,043,7289,025,3749,043,728166,915-16,2589,026,329
1993 (CL)59,337,0999,702,7269,661,1409,702,726365,627-40,6119,673,610
1994 (CL)49,640,09810,422,62110,340,41410,422,621782,523-73,68810,375,605
1995 (CL)39,006,11310,571,47110,475,53310,571,4711,565,35830,96710,512,108
1996 (BF)27,486,11310,490,87210,436,79110,436,7912,950,678-275,68810,387,245
1997 (BF)14,344,14410,933,65810,662,53510,662,5356,318,39110,662,53510,165,481
Total79,798,86892,060,48512,261,617
Total unpaid / IBNR
$12,261,617k
Mack std. error (total)
$550,736k
Mack CV
4.4%

Rate indication

AYUltimate LRTrend yearsTrended LR
198887.3%10.0117.3%
198988.1%9.0114.9%
199085.7%8.0108.6%
199178.2%7.096.2%
199278.9%6.094.2%
199379.3%5.091.9%
199478.5%4.088.3%
199574.8%3.081.8%
199671.2%2.075.5%
199771.4%1.073.6%
3-yr weighted trended LR
87.1%
Indicated: 24.4%
5-yr weighted trended LR
90.0%
Indicated: 28.6%
Credibility Z (premium rule)
1.00
Complement: 28.1%
Credibility-weighted indication (3yr)
24.4%
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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