Exposure curve
Function giving the share of the original premium that goes to a deductible or a layer, based on the size of that layer relative to the insured value. You can price with no loss history at all.
Bernegger, 1997, ASTIN Bulletin: Stefan Bernegger ties the Swiss Re exposure curves to an analytical family, the MBBEFD distribution class. The typical case is an industrial risk with 200M EUR insured value that has never had a claim: no history supports pricing a layer between 20M and 50M EUR. The exposure curve changes the question. It plots the ratio of a loss amount to insured value on the horizontal axis, and on the vertical axis the share of total premium consumed by covering losses up to that amount. A layer rate then reads as a difference between two ordinates. The curve is concave, starts at zero and ends at one, and its curvature describes the relative severity of the risk. A curve rising very fast describes frequent small losses; a flat one describes total destruction risk. It assumes the damage ratio distribution does not depend on risk size, which holds inside a homogeneous occupancy class and fails between a warehouse and a refinery.
Textbook case: an industrial risk with 100M EUR of insured value and 400K EUR of original premium. We price a 20M EUR layer excess of 10M EUR. The selected exposure curve gives G(0.10) = 0.74 and G(0.30) = 0.93. The layer takes 0.93 minus 0.74, or 19% of 400K EUR, so 76K EUR before loadings. And that number comes out without a single claim ever reported on the risk.
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