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)10125,049125,049125,049125,04901,557125,049
1989 (CL)9147,358149,216148,758149,2161,8581,186149,252
1990 (CL)8187,760192,674191,267192,6744,9143,113196,092
1991 (CL)7213,396224,115221,043224,11510,7191,063229,642
1992 (CL)6213,904230,811227,833230,81116,9071,058235,831
1993 (CL)5193,676219,624221,332219,62425,9481,202224,868
1994 (CL)4151,081185,415188,970185,41534,334-708190,572
1995 (CL)3111,268157,873167,076157,87346,605-14,524153,299
1996 (BF)266,033125,746142,121142,12176,088-15,772126,403
1997 (BF)125,265129,150135,599135,599110,334135,599111,592
Total1,434,7901,762,496327,706
Total unpaid / IBNR
$327,706k
Mack std. error (total)
$20,578k
Mack CV
6.7%

Rate indication

AYUltimate LRTrend yearsTrended LR
198870.6%10.094.9%
198974.2%9.096.8%
199078.3%8.099.2%
199178.4%7.096.4%
199267.8%6.081.0%
199352.4%5.060.8%
199450.7%4.057.0%
199546.7%3.051.0%
199649.6%2.052.6%
199755.3%1.056.9%
3-yr weighted trended LR
56.6%
Indicated: -19.1%
5-yr weighted trended LR
67.9%
Indicated: -3.1%
Credibility Z (premium rule)
1.00
Complement: -9.4%
Credibility-weighted indication (3yr)
-19.1%
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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