Two-parameter family representing an exposure curve through a closed form borrowed from statistical physics, which replaced tabulated tables with an interpolable function.
Before 1997, an exposure curve was a table of values, proprietary to each reinsurer, interpolated linearly with no knowledge of what happened between two rows. Stefan Bernegger proposed a two-parameter family, written b and g, of which the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions are special cases, hence the acronym. Its value is threefold. It gives a closed form for the curve and its derivative, so a layer rate is computable exactly at any point. Its two parameters have a concrete reading, g being tied to the probability of total loss and b to the shape of the body of the distribution, which allows calibration from expert judgment when data is missing. And it spans the whole useful domain, from the near linear curve of a proportional loss risk to the total destruction curve. It has become the de facto exchange format between reinsurers and brokers for property risk pricing.
Stefan Bernegger published the MBBEFD model in the ASTIN Bulletin in 1997. On a logistics warehouse class calibrated in 2025, the retained parameters are b equal to 3.1 and g equal to 24, corresponding to a total loss probability near 4% and a curve passing through G(0.10) equal to 0.74. Moving g from 24 to 40, which reflects a doubling of total loss risk, moves the rate of the 20 excess 10M EUR layer from 19% to 23% of original premium.
MBBEFD, Maxwell-Boltzmann Bose-Einstein Fermi-Dirac, courbe de Bernegger, modèle MBBEFD