Product of LDFs from a given development age to ultimate, used to estimate the final charge from current cumulative.
The CDF (cumulative development factor) is the product of all LDFs chained from a given development age to ultimate. Formula: CDF(age n → ultimate) = LDF(n→n+1) × LDF(n+1→n+2) × … × LDF(k→ultimate). The estimated ultimate for an accident year is: Ultimate = Cumulative(age n) × CDF(n→ultimate). IBNR = Ultimate − Cumulative(age n). A CDF above 1 indicates remaining development (the year is not yet run off); a CDF below 1 would be anomalous (except with large recoveries). The CDF at the most recent age (often 12 months for the current accident year) is typically the most uncertain.
Accident year 2023, 12-month cumulative: 2.8 M EUR. CDF 12 months → ultimate = 1.65. Estimated ultimate: 4.62 M EUR. IBNR = 1.82 M EUR.
cumulative development factor, facteur cumulé, tail factor, CDF to ultimate