Taylor separation method

G. C. Taylor published "Separation of inflation and other effects from the distribution of non-life insurance claim delays" in the ASTIN Bulletin in 1977. The method separates, in a payment triangle, the effect of the claim's age from that of the calendar year, where inflation sits. Taylor generalized an idea Verbeek had applied to motor excess of loss treaties. The starting point: a payment triangle mixes two clocks. The age of the claim sets the pattern at which it is paid; the calendar year of payment sets the level of prices, compensation scales and case law. Chain ladder reads along the rows and silently projects whatever average inflation it found in its factors. Taylor writes the incremental payment, divided by the accident year's claim count, as the product of a pattern by age and an index by calendar year. The pattern sums to one; the index is shared by a whole diagonal. Arithmetic separation solves both series diagonal by diagonal, starting from the latest. What remains is to extend the index over future years, and that is where the actuary takes back control. The actuary sets an explicit inflation assumption, drawn from a cost index or a fitted trend, that can be argued with underwriting and finance. That is the whole merit of the method. Its limit sits in the same place. The model assumes a pattern that is stable from one accident year to the next, and a claims department that speeds up settlements produces exactly the diagonal distortion the method will read as inflation. It also needs a reliable claim count per accident year, which low-frequency lines seldom have. Not to be confused with the calendar year effect, the phenomenon the method isolates, nor with claims inflation, its most frequent cause.