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: Erie Ins Exchange 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 | 1.013 | 0.910 | 0.938 | 1.003 | 1.022 | 0.976 | 1.058 | 1.028 | 1.045 |
| CDF to ult. | 0.982 | 0.970 | 1.066 | 1.137 | 1.133 | 1.109 | 1.137 | 1.074 | 1.045 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 32,415 | 1.000 | 32,415 | 0 | 0 | 0.0% |
| AY 2 | 40,712 | 1.045 | 42,535 | 1,823 | 489 | 26.9% |
| AY 3 | 48,428 | 1.074 | 52,017 | 3,589 | 1,326 | 36.9% |
| AY 4 | 59,471 | 1.137 | 67,597 | 8,126 | 3,619 | 44.5% |
| AY 5 | 79,012 | 1.109 | 87,626 | 8,614 | 11,025 | 128.0% |
| AY 6 | 89,257 | 1.133 | 101,150 | 11,893 | 13,904 | 116.9% |
| AY 7 | 88,410 | 1.137 | 100,520 | 12,110 | 15,451 | 127.6% |
| AY 8 | 92,364 | 1.066 | 98,453 | 6,089 | 17,336 | 284.7% |
| AY 9 | 88,980 | 0.970 | 86,268 | -2,712 | 18,445 | -680.0% |
| AY 10 | 90,097 | 0.982 | 88,498 | -1,599 | 22,507 | -1407.9% |
| Total | 709,146 | 757,077 | 47,931 | 59,996 | 125.2% |
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.