Chain-Ladder Development
Project ultimate losses from a loss-development triangle using selectable age-to-age averaging methods, an optional fitted tail, and Mack (1993) standard errors.
Loaded: Allstate Ins Co Grp — Workers' Compensation (incurred, CAS Loss Reserve DB)
| Origin \ Dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| AY 1 | ||||||||||
| AY 2 | ||||||||||
| AY 3 | ||||||||||
| AY 4 | ||||||||||
| AY 5 | ||||||||||
| AY 6 | ||||||||||
| AY 7 | ||||||||||
| AY 8 | ||||||||||
| AY 9 | ||||||||||
| AY 10 |
Development factors
| Age | 1→2 | 2→3 | 3→4 | 4→5 | 5→6 | 6→7 | 7→8 | 8→9 | 9→10 |
|---|---|---|---|---|---|---|---|---|---|
| Method | |||||||||
| Factor | 0.996 | 0.930 | 0.997 | 1.010 | 0.991 | 1.001 | 1.005 | 1.003 | 0.999 |
| CDF to ult. | 0.932 | 0.936 | 1.007 | 1.010 | 1.000 | 1.009 | 1.008 | 1.002 | 0.999 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 347,762 | 1.000 | 347,762 | 0 | 0 | 0.0% |
| AY 2 | 300,620 | 0.999 | 300,279 | -341 | 3,610 | -1058.4% |
| AY 3 | 281,101 | 1.002 | 281,720 | 619 | 4,825 | 778.9% |
| AY 4 | 269,592 | 1.008 | 271,637 | 2,045 | 5,851 | 286.2% |
| AY 5 | 184,940 | 1.009 | 186,586 | 1,646 | 5,398 | 327.9% |
| AY 6 | 96,930 | 1.000 | 96,948 | 18 | 3,976 | 22386.9% |
| AY 7 | 96,185 | 1.010 | 97,139 | 954 | 7,134 | 747.5% |
| AY 8 | 92,314 | 1.007 | 92,917 | 603 | 10,509 | 1741.8% |
| AY 9 | 51,205 | 0.936 | 47,917 | -3,288 | 8,767 | -266.6% |
| AY 10 | 6,725 | 0.932 | 6,265 | -460 | 3,937 | -856.5% |
| Total | 1,727,374 | 1,729,171 | 1,797 | 23,613 | 1314.2% |
IBNR by origin year with Mack std. error
Assumptions & limitations
- Development patterns are stable across origin years and future development follows the same age-to-age factors as historical experience.
- Mack's model assumes the chain-ladder recursion is correctly specified (uncorrelated origin years, no calendar-year trend) and factors are the volume-weighted averages unless overridden per age.
- A fitted exponential-decay tail is an extrapolation; validate against industry benchmarks before relying on it.