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)1027,44527,44527,44527,44503427,445
1989 (CL)927,47027,50427,50127,504345927,516
1990 (CL)830,00430,09230,09030,0928838630,073
1991 (CL)733,72733,64333,63433,643-8442133,926
1992 (CL)639,23739,27139,27239,2713440340,109
1993 (CL)553,35053,98053,89853,9806301654,697
1994 (CL)460,72664,35463,62464,3543,628-62164,934
1995 (CL)354,43263,15961,08363,1598,7274,51961,698
1996 (BF)242,56360,07456,57956,57914,0163,39369,338
1997 (BF)121,07458,05547,62647,62626,55247,62662,690
Total390,028443,65353,625
Total unpaid / IBNR
$53,625k
Mack std. error (total)
$6,787k
Mack CV
10.0%

Rate indication

AYUltimate LRTrend yearsTrended LR
198842.5%10.057.2%
198955.6%9.072.5%
199051.8%8.065.6%
199145.3%7.055.7%
199248.5%6.057.9%
199357.7%5.066.9%
199462.9%4.070.8%
199565.9%3.072.0%
199659.1%2.062.7%
199757.4%1.059.1%
3-yr weighted trended LR
69.9%
Indicated: -0.1%
5-yr weighted trended LR
65.4%
Indicated: -6.6%
Credibility Z (premium rule)
1.00
Complement: -9.0%
Credibility-weighted indication (3yr)
-0.1%
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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