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)10111,727111,727111,727111,7270-661111,727
1989 (CL)9116,055115,372115,560115,372-683-1,826117,658
1990 (CL)8113,243112,504112,690112,504-739-4,687116,719
1991 (CL)7124,352126,118125,721126,1181,766-6,852130,900
1992 (CL)6109,505113,537113,073113,5374,032-4,775125,026
1993 (CL)592,37498,87099,41298,8706,496-8,997110,233
1994 (CL)482,47095,26097,62895,26012,790-12,162107,465
1995 (CL)364,85486,32094,81786,32021,466-25,555108,100
1996 (BF)259,141105,311116,467116,46757,326-19,160132,144
1997 (BF)140,409170,432156,250156,250115,841156,250173,581
Total914,1301,132,425218,295
Total unpaid / IBNR
$218,295k
Mack std. error (total)
$28,795k
Mack CV
13.0%

Rate indication

AYUltimate LRTrend yearsTrended LR
198861.6%10.082.8%
198962.2%9.081.2%
199060.3%8.076.4%
199158.2%7.071.6%
199251.0%6.060.9%
199341.7%5.048.3%
199438.1%4.042.9%
199532.3%3.035.3%
199640.2%2.042.7%
199746.4%1.047.8%
3-yr weighted trended LR
41.9%
Indicated: -40.1%
5-yr weighted trended LR
50.8%
Indicated: -27.4%
Credibility Z (premium rule)
1.00
Complement: -25.1%
Credibility-weighted indication (3yr)
-40.1%
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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