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: California Cas 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 | 1.008 | 0.992 | 0.970 | 0.969 | 0.983 | 0.981 | 0.968 | 0.964 | 0.996 |
| CDF to ult. | 0.842 | 0.835 | 0.842 | 0.868 | 0.896 | 0.912 | 0.929 | 0.960 | 0.996 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 53,261 | 1.000 | 53,261 | 0 | 0 | 0.0% |
| AY 2 | 48,300 | 0.996 | 48,109 | -191 | 1,934 | -1010.0% |
| AY 3 | 56,971 | 0.960 | 54,697 | -2,274 | 3,613 | -158.9% |
| AY 4 | 70,532 | 0.929 | 65,550 | -4,982 | 4,545 | -91.2% |
| AY 5 | 67,845 | 0.912 | 61,847 | -5,998 | 4,506 | -75.1% |
| AY 6 | 67,697 | 0.896 | 60,658 | -7,039 | 4,536 | -64.4% |
| AY 7 | 69,720 | 0.868 | 60,521 | -9,199 | 4,801 | -52.2% |
| AY 8 | 79,381 | 0.842 | 66,815 | -12,566 | 6,032 | -48.0% |
| AY 9 | 73,181 | 0.835 | 61,118 | -12,063 | 5,881 | -48.8% |
| AY 10 | 50,171 | 0.842 | 42,242 | -7,929 | 5,794 | -73.1% |
| Total | 637,059 | 574,819 | -62,240 | 25,414 | -40.8% |
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.