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: Allstate Ins Co 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 | 2.223 | 1.338 | 1.158 | 1.093 | 1.059 | 1.046 | 1.031 | 1.036 | 1.011 |
| CDF to ult. | 4.501 | 2.025 | 1.514 | 1.307 | 1.196 | 1.130 | 1.080 | 1.047 | 1.011 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 325,322 | 1.000 | 325,322 | 0 | 0 | 0.0% |
| AY 2 | 273,873 | 1.011 | 276,864 | 2,991 | 9,169 | 306.6% |
| AY 3 | 256,788 | 1.047 | 268,961 | 12,173 | 13,187 | 108.3% |
| AY 4 | 239,195 | 1.080 | 258,402 | 19,207 | 14,867 | 77.4% |
| AY 5 | 159,496 | 1.130 | 180,151 | 20,655 | 13,481 | 65.3% |
| AY 6 | 87,215 | 1.196 | 104,286 | 17,071 | 10,533 | 61.7% |
| AY 7 | 91,077 | 1.307 | 119,003 | 27,926 | 12,575 | 45.0% |
| AY 8 | 87,311 | 1.514 | 132,157 | 44,846 | 17,394 | 38.8% |
| AY 9 | 44,916 | 2.025 | 90,948 | 46,032 | 23,930 | 52.0% |
| AY 10 | 691 | 4.501 | 3,110 | 2,419 | 8,780 | 362.9% |
| Total | 1,565,884 | 1,759,204 | 193,320 | 58,633 | 30.3% |
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.