Ratio of cumulative losses at two successive development ages, the building block of the chain ladder method.
A loss development factor (LDF or age-to-age factor) is the ratio of cumulative losses at a given development age to cumulative losses at the prior development age, for the same accident year. LDF(n→n+1) = Cumulative(n+1) / Cumulative(n). On a run-off triangle, LDFs are calculated for each accident year and column, then averaged (simple average, weighted, median) to obtain representative LDFs. They are then chained to obtain the CDF (cumulative development factor to ultimate). An LDF close to 1 indicates little residual development; a high LDF signals a long-tailed line. Analyzing LDFs by accident year helps detect behavioral changes or atypical losses.
Motor liability triangle: LDF 12→24 months = 1.45; LDF 24→36 = 1.18; LDF 36→48 = 1.07; LDF 48→ultimate = 1.02. CDF from 12 months = 1.45 × 1.18 × 1.07 × 1.02 ≈ 1.86.
loss development factor, facteur de développement, age-to-age factor, link ratio