Paid-to-incurred ratio

Berquist and Sherman published in 1977, in the Proceedings of the Casualty Actuarial Society, the method that adjusts a triangle when case reserve adequacy or settlement speed has changed. The first signal they rely on comes down to one division. The paid-to-incurred ratio divides, for each accident year and each age, cumulative paid losses by reported incurred, paid plus case reserves. Read down a column, at equal age, it should stay stable from one year to the next. When it falls on the latest diagonals, two readings compete: either claims management has strengthened case reserves and incurred is rising faster than before, or payments are slowing. The ratio alone does not settle it. You cross it with closed claim counts over reported counts, which measures settlement speed, and with the average case reserve per open claim, adjusted for inflation, which measures reserve level. Once the cause is known, the choice follows. Case strengthening distorts incurred chain ladder, which applies old factors calibrated on underreserved files and counts the same strengthening twice. Paid chain ladder stays sound as long as the payment pattern has not moved. Slower settlement distorts the other one. Munich chain ladder, by Quarg and Mack in 2004, turns this ratio into a model variable instead of a side check. It has a blind spot: a book whose coverage mix shifts toward heavy, slow-settling claims sees the ratio drop with no change in claims practice at all. Not to be confused with the loss ratio, which divides incurred by premium, or with the settlement pattern itself.