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)10205,921205,921205,921205,921010205,921
1989 (CL)9227,553227,564227,562227,56411-114227,567
1990 (CL)8260,062260,166260,145260,166104-401260,647
1991 (CL)7266,822267,241267,190267,241419-298267,228
1992 (CL)6288,748289,971289,871289,9711,223757291,031
1993 (CL)5307,179310,575310,322310,5753,396-1,389311,353
1994 (CL)4334,928344,294343,254344,2949,366-1,748345,797
1995 (CL)3337,595361,649359,294361,64924,0541,622367,921
1996 (BF)2306,832368,275363,191363,19156,359977375,078
1997 (BF)1196,865393,129370,823370,823173,958370,823374,519
Total2,732,5053,001,395268,890
Total unpaid / IBNR
$268,890k
Mack std. error (total)
$13,049k
Mack CV
4.4%

Rate indication

AYUltimate LRTrend yearsTrended LR
198879.7%10.0107.1%
198982.1%9.0107.1%
199082.3%8.0104.2%
199174.4%7.091.5%
199271.1%6.084.9%
199370.6%5.081.8%
199473.5%4.082.7%
199572.4%3.079.1%
199670.2%2.074.5%
199769.5%1.071.6%
3-yr weighted trended LR
81.1%
Indicated: 15.9%
5-yr weighted trended LR
83.6%
Indicated: 19.4%
Credibility Z (premium rule)
1.00
Complement: 16.0%
Credibility-weighted indication (3yr)
15.9%
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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