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CDF: Cumulative development factor

The product of LDFs from a given development age to ultimate. Applied to current cumulative losses, it gives the estimated ultimate.

Definition

Mack, 1993, ASTIN Bulletin: Thomas Mack derives the standard error of chain ladder reserves without any distributional assumption, so every development factor now comes with an error bar. The CDF (cumulative development factor) is the product of the LDFs chained from a given development age to ultimate: CDF(n → ultimate) = LDF(n→n+1) × LDF(n+1→n+2) × … × LDF(k→ultimate). Then Ultimate = Cumulative(n) × CDF(n→ultimate) and IBNR = Ultimate − Cumulative(n). A CDF above 1 means development remains and the year has not run off. Below 1 it would be anomalous, unless there are large recoveries. The CDF at the youngest age, often 12 months for the current accident year, is usually the most uncertain.

Its 5 cross-references, woven across the glossary's 18 categories
CDF: Cumulative development factor: Actuarial science glossary illustration, AlgoPolis
Example

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.

Read next
Actuarial scienceLDF: Loss development factorRatio of cumulative losses at two successive development ages, the building block of the chain ladder method.Read the entry →Actuarial scienceChain ladderReserving method that projects each accident year to its ultimate cost by applying the development factors observed on older accident years.Read the entry →Actuarial scienceUltimate lossThe estimated total cost of claims for an accident year once all development is complete, including IBNR and residual reserves.Read the entry →
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QuizEstimating what a year of claims will costAcademy questions on this concept, each one marked and explained.Test yourself →
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