First loss scale
Table giving the percentage of premium corresponding to cover limited to a fraction of insured value, the tabulated ancestor of the exposure curve and still in use in several markets.
Ruth Salzmann published in 1963, in the Proceedings of the Casualty Actuarial Society ("Rating by Layer of Insurance"), tables drawn from US homeowners losses that remain the most cited reference of their kind. The principle: a policyholder covering only the first 10% of a plant's value pays well over 10% of the full premium, because that first slice concentrates most of the frequency. The first loss scale quantifies that relationship and returns a percentage of premium per percentage of value covered. It carries the same information as an exposure curve, set out as a table and read in the other direction: the curve serves a reinsurer pricing a high layer, the scale serves a direct insurer pricing a low limit. In industrial property the market also uses German and Swiss tables. Their limit is structural. A table calibrated thirty years ago ignores rebuilding cost inflation and value concentration, and reading it today without recalibration amounts to pricing with another era's loss experience.
Ruth Salzmann published her homeowners loss distribution tables in 1963, in the Proceedings of the Casualty Actuarial Society, and they served as a market reference in the United States for several decades. On a European industrial table calibrated in 2024, cover limited to 10% of insured value consumes 62% of the full premium, and cover limited to 25% consumes 84%: the remaining three quarters of value carry only 16% of the rate.
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