Claims development result (CDR)

At December 31, 2024, the best estimate of a line's outstanding claims is 20 million euros. A year later, 8 million has been paid on those same claims and the estimate of the remainder is 13.1 million. The gap, 20 − (8 + 13.1) = −1.1 million, is the claims development result (CDR): negative, adverse development; positive, a release. Chain ladder and Mack reason to ultimate, over the whole life of the claims. Solvency II reasons over one year: Article 101 of the directive calibrates the SCR to a 99.5% value at risk over a one-year horizon. Reserve risk there is the possible loss on that CDR. Michael Merz and Mario Wüthrich published "Modeling the Claims Development Result for Solvency Purposes" in the CAS E-Forum in Fall 2008. Within the Mack framework, they give a closed formula for the mean squared error of prediction of the observable CDR, by accident year and in total. It is smaller than Mack's error on the ultimate, since only the coming year's diagonal is revealed and the uncertainty of later ones stays beyond the horizon. On a long tail line the gap is wide. The framework inherits Mack's assumptions, independence of accident years included, and misses an inflation that would hit every diagonal at once. Internal models often do the same thing by simulation, drawing the next year and then rerunning the whole reserving calculation on the completed triangle (re-reserving, or actuary in the box). The result then depends on the method assumed at the next closing, which has to be documented. Not to be confused with accounting prior year development, which records the same gap after the fact on carried reserves, nor with the Mack method, which measures uncertainty to ultimate.