Frequency-severity reserving method

A motor bodily injury book counts its victims within months but takes years to learn what they cost: medical consolidation comes late, the French Dintilhac nomenclature prices loss by loss item, attendant care is capitalized. Chain ladder on incurred blends those two speeds. The frequency-severity method separates them. Claim counts are projected on a triangle of reported counts, which settles quickly. The average cost is projected on a triangle of severities, paid per closed claim or incurred per reported claim. The ultimate is their product. For the young accident year, whose severity says nothing yet, the average cost of mature years is taken and brought to the target year's level with a claims inflation trend. That trend becomes the main assumption of the method. Fisher and Lange gave a classic version, organized by report year, in the Proceedings of the CAS in 1973. The method holds on high volume lines, where counts are large and definitions stable. It breaks when the definition of a claim moves (closed without payment counted or not, one claimant or one occurrence) and when the mix shifts under the average. It also breaks on large losses, which are taken out above a threshold and handled file by file because a single one moves the year's average. It also works as a check: a chain ladder ultimate that implies a frequency or a severity outside any past series shows up at once. Not to be confused with the frequency and severity framework of pricing, which bears on the claims of future policies, nor with the average cost as a monitoring indicator.