A Robustification of the Chain-Ladder Method

In a non-life insurance business an insurer often needs to build up a reserve to be able to meet his future obligations arising from claims that are known to exist, but for which the actual size is unknown at the time the reserves have to be set. The delay of the actual payment of the claims is, for example, due to long legal procedures or difficulties in determining the size of the claims. Therefore, insurers have to build up reserves enabling them to pay the outstanding claims and to meet claims arising in the future on the written contracts. We assume that Xij and Cij (for 1 ≤ i, j ≤ n) are respectively the incremental and the cumulative claims amount of accident year i and development year j. Furthermore let Ri and R respectively define the outstanding claims reserve of accident year i and the overall reserve. For representation of the data it is common to use a run-off triangle as in Table 1.