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: Lumbermens Underwriting Alliance — Workers' Compensation (paid, 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 | 2.229 | 1.413 | 1.138 | 1.075 | 1.028 | 1.016 | 1.008 | 1.009 | 1.007 |
| CDF to ult. | 4.122 | 1.849 | 1.308 | 1.149 | 1.069 | 1.040 | 1.024 | 1.016 | 1.007 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 75,655 | 1.000 | 75,655 | 0 | 0 | 0.0% |
| AY 2 | 70,846 | 1.007 | 71,358 | 512 | 180 | 35.1% |
| AY 3 | 49,994 | 1.016 | 50,793 | 799 | 301 | 37.7% |
| AY 4 | 41,970 | 1.024 | 42,969 | 999 | 293 | 29.3% |
| AY 5 | 36,884 | 1.040 | 38,361 | 1,477 | 312 | 21.1% |
| AY 6 | 20,813 | 1.069 | 22,257 | 1,444 | 404 | 28.0% |
| AY 7 | 14,570 | 1.149 | 16,746 | 2,176 | 2,030 | 93.3% |
| AY 8 | 10,439 | 1.308 | 13,658 | 3,219 | 2,713 | 84.3% |
| AY 9 | 8,768 | 1.849 | 16,214 | 7,446 | 3,678 | 49.4% |
| AY 10 | 5,258 | 4.122 | 21,676 | 16,418 | 4,873 | 29.7% |
| Total | 335,197 | 369,687 | 34,490 | 7,393 | 21.4% |
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.