Berquist-Sherman method
Two triangle adjustments, published in 1977, that restate incurred at the current level of case reserve adequacy and paid at a constant settlement rate, before any projection is run.
Berquist and Sherman published "Loss Reserve Adequacy Testing: A Comprehensive, Systematic Approach" in the Proceedings of the Casualty Actuarial Society in 1977. Their method corrects the triangle before projecting it. Every actuary has met the problem it addresses on the day a claims department changed its instructions. Chain ladder assumes that the way claims are reserved and settled stays the same from one diagonal to the next; when it changes, the development factors blend the old regime with the new one. The first adjustment targets case reserve adequacy. Take the average case reserve per open claim on the latest diagonal and bring it back to earlier diagonals with a severity trend. Then rebuild incurred as paid plus open count times that restated average. The triangle then shows what incurred would have been had handlers always reserved at today's level. The second targets the settlement rate. Compute the disposal rates (closed counts over ultimate counts) on the latest diagonal and impose them on every accident year. Cumulative paid is then interpolated on those closed counts, linearly or along an exponential curve. Each rests on an input taken from outside the triangle being corrected: the severity trend for one, the ultimate claim count for the other. A poorly chosen trend moves the ultimate as much as the distortion it was meant to remove. Diagnosis comes first: paid to incurred ratios, average open case reserve by age, disposal rates, read along the diagonals. With no visible break, nothing is adjusted. Not to be confused with Munich chain ladder, which reconciles paid and incurred without restating the data.
Textbook case: accident year 2023 at 12 months, 400,000 euros paid and 100 open claims reserved at an average of 8,000 euros, incurred of 1.2 million. On the latest diagonal, accident year 2025 at 12 months carries an average open case reserve of 12,000 euros. With a severity trend of 5% a year, the restated 2023 average is 12,000 / 1.05² = 10,884 euros. Adjusted incurred: 400,000 + 100 × 10,884 = 1,488,400 euros, 24% above the original figure. Reserve strengthening no longer reads as development, and the recomputed 12 to 24 month factor comes down accordingly.
Berquist-Sherman technique, Berquist-Sherman adjustment, case reserve adequacy adjustment, settlement rate adjustment
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