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)1060,51660,51660,51660,516020460,516
1989 (CL)965,51165,73365,69065,7332221,04665,212
1990 (CL)862,62663,36363,26063,363737-1062,896
1991 (CL)764,51866,12165,96566,1211,603-18765,849
1992 (CL)674,04877,78176,97277,7813,7336077,074
1993 (CL)553,59957,65657,30357,6564,0571,34957,649
1994 (CL)454,38862,45362,32962,4538,06554962,554
1995 (CL)349,83565,10565,80365,10515,27036977,372
1996 (BF)244,37777,43277,12477,12432,747-7,770103,595
1997 (BF)127,309118,44294,17394,17366,86494,173113,280
Total556,727690,024133,297
Total unpaid / IBNR
$133,297k
Mack std. error (total)
$46,707k
Mack CV
29.6%

Rate indication

AYUltimate LRTrend yearsTrended LR
198866.0%10.088.7%
198971.5%9.093.3%
199067.1%8.084.9%
199164.0%7.078.7%
199273.7%6.088.0%
199363.2%5.073.3%
199458.6%4.066.0%
199555.2%3.060.3%
199658.0%2.061.6%
199762.6%1.064.4%
3-yr weighted trended LR
66.0%
Indicated: -5.8%
5-yr weighted trended LR
72.9%
Indicated: 4.2%
Credibility Z (premium rule)
1.00
Complement: 4.3%
Credibility-weighted indication (3yr)
-5.8%
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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