Generalized linear model (GLM)
A family of statistical models generalizing linear regression, now the standard for non-life pricing and risk segmentation.
John Nelder and Robert Wedderburn, Journal of the Royal Statistical Society, 1972: linear regression extended to variables that are not normally distributed, through a link function and a distribution from the exponential family. In non-life pricing the setup became standard practice: frequency as Poisson with a log link, severity as gamma, or pure premium in one go as Tweedie, with exposure as an offset. The log link makes the rating plan multiplicative, and each coefficient reads as a relativity: 1.18 for an industry means 18% more expected losses, other variables held equal. The Casualty Actuarial Society made it the subject of its reference monograph in 2016 (Goldburd, Khare and Tevet). The GLM held its ground against more powerful machine learning models because it can be filed, explained to a regulator and adjusted by hand. Its weakness is the interaction nobody wrote in, which the model will not find on its own. In cyber it runs into the data first: a few hundred claims a year, on a risk that changes quickly, cannot support thirty coefficients, and underwriting judgment takes over from the statistics.
Hypothetical case: an actuary uses a generalized linear model to estimate how industry, company size and the presence of multi-factor authentication separately influence the frequency of cyber losses, to build a segmented rating plan.
GLM, generalised linear model, generalized linear model
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