Generalized linear model (GLM)

The generalized linear model is a family of statistical models that extends classic linear regression by adapting it to variables that do not follow a normal law, which is precisely the case of insurance quantities such as claim frequency, often modeled by a Poisson law, or their severity, modeled by a gamma law. Through a link function connecting the prediction to the explanatory variables, the model estimates the specific influence of each risk factor, age, sector, size, security measures, on the expected loss experience. This approach has become the standard for non-life pricing, because it allows a fine, statistically grounded segmentation, isolating the effect of each variable all else being equal. It remains valued for its transparency and interpretability, important qualities in the face of regulators and for understanding the portfolio, where more powerful machine-learning models are often more opaque. In cyber insurance, however, the application of generalized linear models runs into the scarcity and instability of data, which limit the reliability of estimates and often require statistics to be supplemented by expert judgment.

An actuary uses a generalized linear model to estimate how the sector of activity, the size of the company and the presence of multi-factor authentication separately influence the frequency of cyber losses, in order to build a segmented pricing.

GLM, modèle linéaire généralisé, generalised linear model