Chain ladder

The chain ladder method arranges cumulative claims in a loss development triangle, accident years in rows and development age in columns, and computes a development factor for each step from one age to the next: the sum of one column divided by the sum of the previous one, over the accident years that have both. Multiplied together up to the last age, these factors give the cumulative factor that takes each open accident year to its ultimate, and the gap between that ultimate and the known incurred is the IBNR reserve. Thomas Mack, ASTIN Bulletin, 1993, gave it a distribution-free model that reproduces those factors exactly and adds what they lacked, a standard error on the reserve. The weakness is that the method multiplies what it sees. A large claim reported early on the youngest year is projected as if it spoke for the whole year, and a change in case reserving practice reads as a change in the risk. Hence the pairing with Bornhuetter-Ferguson on recent years, which keeps the factors but not the projection, and the tail beyond the last observed age, set separately through a tail factor. A worked chain ladder solution checks out in a few lines, as in the example below.