Machine Learning Case Notes: Logistic Regression and Machine Learning in Python for Actuarial Science

Actuarial science sits at the intersection of mathematics, statistics, finance, and risk management, where the goal is to quantify uncertain future events and translate them into sound financial decisions. Whether estimating mortality rates for life insurance, predicting lapse behaviour, or modelling the frequency of motor claims, actuaries rely heavily on statistical tools capable of transforming raw data into credible estimates of risk. Among these tools, logistic regression remains one of the most powerful and widely used methods. Its strength lies not just in prediction, but in the ability to provide a clear, interpretable relationship between risk factors and event probabilities—an essential requirement for pricing, reserving, capital modelling, experience studies, and regulatory compliance.

The last decade has seen a surge in richer datasets: telematics signals, behavioural indicators, medical diagnostics, digital payment patterns, climate-linked exposures, and detailed customer interactions. As the actuarial profession expands into data science and machine learning, the need for robust and transparent predictive models has become even more important. Logistic regression offers an ideal starting point—it is mathematically simple, statistically principled, and flexible enough to incorporate nonlinearities, interactions, and regularisation techniques. It also integrates seamlessly with more advanced machine-learning workflows, making it suitable for both traditional actuarial modelling frameworks and modern data-driven approaches.

In practice, actuaries must ensure that models are not only accurate but also explainable and fit for purpose. Pricing actuaries must justify how risk factors influence premiums; reserving actuaries must validate that selected assumptions align with observed experience; and capital modellers must demonstrate that estimated probabilities are well-calibrated and stable. Logistic regression provides this transparency: coefficients translate directly into odds ratios, enabling clear interpretation of how age, health status, driving behaviour, or policy features affect risk. When paired with ROC curves, calibration plots, and probability distributions, the model provides a complete analytical story from data input to business decision.

This guide provides an end-to-end, practical demonstration of logistic regression and basic machine-learning techniques within an actuarial context. Through three realistic simulated case studies—life insurance mortality, policy lapse (persistency), and motor insurance claim frequency—you will learn how to build predictive models, prepare and scale features, interpret model coefficients, and evaluate performance using multiple diagnostic figures. These examples mirror real actuarial workflows and can serve as templates for experience studies, GLM-based pricing, assumption setting, and predictive analytics projects. Whether you are a student, a practising actuary, or a data science professional working with insurance portfolios, this guide offers a solid foundation for applying logistic regression effectively within actuarial science.

Below is a step-by-step guide showing how to use logistic regression and basic machine learning techniques in Python for common actuarial science problems, with simulated data and multiple analytical figures for each case study.

The three case studies:

1. Life Insurance Mortality Risk – probability of death within a fixed horizon

2. Policy Lapse (Persistency) Risk – probability of policy surrender

3. Motor Insurance Claim Risk – probability of at least one claim next year

At the end, you’ll find a single end-to-end script you can copy, paste, and run.

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