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 (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 | 0.964 | 0.953 | 0.965 | 1.017 | 1.004 | 1.003 | 1.004 | 1.005 | 1.004 |
| CDF to ult. | 0.920 | 0.954 | 1.001 | 1.038 | 1.021 | 1.016 | 1.014 | 1.010 | 1.004 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 78,078 | 1.000 | 78,078 | 0 | 0 | 0.0% |
| AY 2 | 73,194 | 1.004 | 73,523 | 329 | 560 | 170.5% |
| AY 3 | 52,068 | 1.010 | 52,569 | 501 | 664 | 132.5% |
| AY 4 | 45,141 | 1.014 | 45,758 | 617 | 701 | 113.7% |
| AY 5 | 42,090 | 1.016 | 42,780 | 690 | 1,055 | 152.9% |
| AY 6 | 38,629 | 1.021 | 39,428 | 799 | 1,208 | 151.3% |
| AY 7 | 33,838 | 1.038 | 35,109 | 1,271 | 2,208 | 173.7% |
| AY 8 | 37,861 | 1.001 | 37,917 | 56 | 4,124 | 7374.7% |
| AY 9 | 25,572 | 0.954 | 24,400 | -1,172 | 4,082 | -348.4% |
| AY 10 | 25,728 | 0.920 | 23,663 | -2,065 | 4,379 | -212.1% |
| Total | 452,199 | 453,224 | 1,025 | 8,789 | 857.6% |
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.