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)10193,499193,499193,499193,49902,979193,499
1989 (CL)9199,997203,124202,732203,1243,1274,317200,480
1990 (CL)8224,078229,193228,268229,1935,1153,782225,430
1991 (CL)7204,911211,401210,783211,4016,4903,505206,719
1992 (CL)6208,008218,032217,047218,03210,0244,684214,524
1993 (CL)5219,345238,547235,816238,54719,202697233,365
1994 (CL)4212,446246,282242,450246,28233,836-1,164244,280
1995 (CL)3190,974252,280246,695252,28061,3066,760240,184
1996 (BF)2143,590243,622239,595239,59596,005-2,227237,368
1997 (BF)175,827247,080237,848237,848162,021237,848230,775
Total1,872,6752,269,801397,126
Total unpaid / IBNR
$397,126k
Mack std. error (total)
$18,264k
Mack CV
4.5%

Rate indication

AYUltimate LRTrend yearsTrended LR
198867.6%10.090.8%
198965.8%9.085.8%
199070.2%8.088.9%
199163.6%7.078.2%
199263.8%6.076.1%
199367.0%5.077.7%
199464.8%4.073.0%
199563.3%3.069.1%
199658.9%2.062.5%
199758.5%1.060.3%
3-yr weighted trended LR
73.1%
Indicated: 4.5%
5-yr weighted trended LR
74.6%
Indicated: 6.6%
Credibility Z (premium rule)
1.00
Complement: 4.3%
Credibility-weighted indication (3yr)
4.5%
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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