Glossary · method
Chain-Ladder Method
Classical actuarial loss-reserving method that derives development factors from cumulative ratios in a loss development triangle.
Chain LadderCLLoss-Development MethodMack 1993
The chain-ladder method is the classical actuarial loss-development model, in use since 1934. Age-to-age factors are computed as ratios of cumulative amounts between successive development periods on a loss development triangle; these factors are projected forward to estimate the ultimate loss for each accident year. The method rests on three implicit assumptions: (1) the development pattern is proportional across accident years, (2) accident years are independent, (3) development factors are stable. Mack (1993) added a distribution-free stochastic structure so the standard error can be computed analytically. Strengths: simple, transparent, works with limited data. Weaknesses: fragile to inflation swings, claim-handling policy changes and external shocks. Diagnostics (residual plot, calendar-year effect, age-to-age trend) are mandatory — without them, broken patterns go undetected. Because the method is volatile for recent accident years, it is typically combined with Bornhuetter-Ferguson for those cohorts.
Örnek
An auto insurer computes age-to-age factors of 2.40, 1.35, 1.12, 1.05, 1.02, 1.01, 1.00 on an 8x8 paid triangle; the cumulative development factor is about 3.85; for accident year 2024 with 12 months of cumulative paid losses of 100M, the ultimate loss is estimated at 385M and the reserve at 285M.