Generalised linear model (GLM)

Category: AI in insurance · Reviewed by Chrissie Anderson, Client Executive · Last reviewed 2026-06-10

A generalised linear model (GLM) is a statistical model in which a linear combination of explanatory variables is mapped, via a link function, to the expected value of a response variable drawn from an exponential-family distribution. In United Kingdom general insurance, GLMs have been the workhorse of personal-lines pricing since the late 1990s, particularly for motor and household frequency-severity modelling.

Category: AI in insurance · Aliases: GLM, GLM pricing · Established: Theoretical foundation Nelder & Wedderburn (1972); insurance adoption in UK from late 1990s · Related: Machine learning underwriting, Gradient boosting machine (GBM), AI underwriting

Definition

A GLM extends ordinary linear regression by:

• allowing the response to follow any distribution in the exponential family (Poisson, gamma, Tweedie, binomial); and
• relating the linear predictor to the mean of the response through a link function (log, logit, identity).

In insurance, claim frequency is conventionally modelled as Poisson with a log link, severity as gamma with a log link, and combined pure premium (frequency × severity) as Tweedie with a log link. The result is a multiplicative tariff that is straightforward to deploy in a rating engine, to audit, and to explain to an underwriter.

Legal / Regulatory basis

• PRA Solvency II: a GLM used in technical provisions or in an internal model must meet documentation, validation and use-test standards under the Solvency II Directive (2009/138/EC) as on-shored.
• FCA Handbook SYSC 4 and ICOBS 6B (general insurance pricing): GLMs used for retail pricing must respect the 2022 price-walking remedy and the Consumer Duty fair-value outcome.
• Institute and Faculty of Actuaries (IFoA): a long sequence of GIRO and Sessional papers from the late 1990s onward standardised UK actuarial practice on GLM pricing; the IFoA’s Practising Certificates and TAS 100 / 200 (Technical Actuarial Standards) impose professional standards on the GLM’s construction and use.
• FCA & PRA DP5/22 / FS2/23: GLMs are explicitly recognised as a form of “AI/ML” for governance purposes, even though they pre-date the modern AI label.

How it works in practice

A UK personal-lines GLM build typically proceeds:

1. One-way analysis of each candidate variable against claim frequency and severity.
2. Banding and grouping of continuous and categorical variables to ensure adequate exposure per cell.
3. Stepwise model build with a Poisson-frequency and gamma-severity pair, or a Tweedie combined model, fitted by iteratively re-weighted least squares.
4. Interaction testing to capture, for example, age × vehicle group in motor.
5. Diagnostics: deviance, residual analysis, lift charts, double-lift against a challenger model.
6. Documentation: variable factors, base level, link function, dispersion, exposure measure and limitations — required under Solvency II Article 125 internal-model documentation standards and good practice under TAS 100.
7. Deployment as a set of multiplicative relativities in the rating engine, with a clear audit trail.

Common variations / Subsequent developments

• Tweedie GLM modelling pure premium directly.
• GLMs with credibility / mixed effects (GLMM) for low-exposure rating cells, particularly in commercial lines.
• Elastic-net regularisation of GLMs to manage high-dimensional factor sets.
• GLM-as-baseline: even where a GBM or neural network is the production model, UK insurers typically maintain a GLM as the reference and challenger.
• GLM in commercial lines: long-established in fleet, employers’ liability and SME packages, often combined with judgement-based loadings.

Example

A UK motor insurer fits a Poisson GLM to third-party-bodily-injury claim frequency, with explanatory variables including driver age, licence years, vehicle group, postcode rating area and annual mileage. A separate gamma GLM is fitted to severity. The product gives a base technical price per policy. The model is signed off by a Chief Actuary holding the SMF-20 controlled function, with model documentation referenced in the Solvency II ORSA.

See also

• Machine learning underwriting
• Gradient boosting machine (GBM)
• AI underwriting (batch 12 expansion)
• Algorithmic underwriting

References

• Nelder, J.A. & Wedderburn, R.W.M., “Generalized Linear Models”, Journal of the Royal Statistical Society A, 1972.
• Institute and Faculty of Actuaries, GIRO Working Party reports on GLM pricing, multiple years.
• Institute and Faculty of Actuaries, TAS 100 — Principles for Technical Actuarial Work.
• Solvency II Directive (2009/138/EC), Article 125, on-shored, https://www.legislation.gov.uk
• FCA & PRA, DP5/22 and FS2/23 — AI and Machine Learning, October 2022 / October 2023.
• FCA, PS21/5 — General Insurance Pricing Practices, May 2021 (ICOBS 6B).

This entry is part of the Apex Insurance Wiki. Last reviewed by Matt Bartlett on 2026-06-10. Next review: 2026-12-10.

Apex Insurance Brokers Limited. Authorised and regulated by the Financial Conduct Authority, FRN 724952. Registered in England and Wales, Companies House 07014570. This entry provides general information about UK insurance concepts and is not regulated advice. Consult your insurance broker on your specific position.