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)10325,322325,322325,322325,32203,514325,322
1989 (CL)9273,873276,864277,503276,8642,991-8,197277,574
1990 (CL)8256,788268,961268,180268,96112,173-9,026263,000
1991 (CL)7239,195258,402260,152258,40219,207-12,911248,319
1992 (CL)6159,496180,151185,512180,15120,655-9,519168,844
1993 (CL)587,215104,286116,769104,28617,071-10,58090,686
1994 (CL)491,077119,003127,823119,00327,926-21,09494,730
1995 (CL)387,311132,157131,911132,15744,846-23,42391,161
1996 (BF)244,91690,94887,31787,31742,401-22,75249,255
1997 (BF)16913,1106,0356,0355,3446,0352,909
Total1,565,8841,758,498192,614
Total unpaid / IBNR
$192,614k
Mack std. error (total)
$58,633k
Mack CV
30.3%

Rate indication

AYUltimate LRTrend yearsTrended LR
198882.4%10.0110.8%
198974.0%9.096.5%
199095.9%8.0121.5%
199182.3%7.0101.2%
199271.3%6.085.1%
199351.9%5.060.1%
199468.2%4.076.8%
199590.3%3.098.7%
199693.6%2.099.3%
1997 (excl.)0.0%1.00.0%
3-yr weighted trended LR
76.5%
Indicated: 9.3%
5-yr weighted trended LR
85.6%
Indicated: 22.3%
Credibility Z (premium rule)
1.00
Complement: 14.7%
Credibility-weighted indication (3yr)
9.3%
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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