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 (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 | 2.031 | 1.297 | 1.148 | 1.087 | 1.049 | 1.037 | 1.023 | 1.009 | 1.005 |
| CDF to ult. | 3.709 | 1.827 | 1.408 | 1.227 | 1.129 | 1.076 | 1.038 | 1.014 | 1.005 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 26,113 | 1.000 | 26,113 | 0 | 0 | 0.0% |
| AY 2 | 34,988 | 1.005 | 35,168 | 180 | 243 | 134.7% |
| AY 3 | 41,015 | 1.014 | 41,604 | 589 | 388 | 65.8% |
| AY 4 | 50,439 | 1.038 | 52,338 | 1,899 | 578 | 30.4% |
| AY 5 | 63,051 | 1.076 | 67,843 | 4,792 | 713 | 14.9% |
| AY 6 | 67,202 | 1.129 | 75,840 | 8,638 | 962 | 11.1% |
| AY 7 | 61,579 | 1.227 | 75,539 | 13,960 | 1,306 | 9.4% |
| AY 8 | 55,908 | 1.408 | 78,715 | 22,807 | 1,723 | 7.6% |
| AY 9 | 42,087 | 1.827 | 76,878 | 34,791 | 1,969 | 5.7% |
| AY 10 | 22,408 | 3.709 | 83,119 | 60,711 | 3,556 | 5.9% |
| Total | 464,790 | 613,158 | 148,368 | 6,693 | 4.5% |
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.