# Neural networks for insurance pricing with frequency and severity data: a benchmark study from data preprocessing to technical tariff

arXiv: https://arxiv.org/abs/2310.12671 · HTML: https://mlsanity.com/paper/2310.12671/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 62 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determination](https://mlsanity.com/paper/2108.03210/) (2021)
- [Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings](https://mlsanity.com/paper/1503.08195/) (2015)
- [Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning](https://mlsanity.com/paper/2103.03635/) (2021)
- [Boosting insights in insurance tariff plans with tree-based machine learning methods](https://mlsanity.com/paper/1904.10890/) (2019)
- [Model Comparison and Calibration Assessment: User Guide for Consistent Scoring Functions in Machine Learning and Actuarial Practice](https://mlsanity.com/paper/2202.12780/) (2022)
- [Insurance Premium Prediction via Gradient Tree-Boosted Tweedie Compound Poisson Models](https://mlsanity.com/paper/1508.06378/) (2015)

## Built on by (most cited first, 7 of 7)

- [Enhancing Actuarial Non-Life Pricing Models via Transformers](https://mlsanity.com/paper/2311.07597/) (2023)
- [From Point to probabilistic gradient boosting for claim frequency and severity prediction](https://mlsanity.com/paper/2412.14916/) (2024)
- [Model Monitoring: A General Framework with an Application to Non-life Insurance Pricing](https://mlsanity.com/paper/2510.04556/) (2025)
- [Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurance](https://mlsanity.com/paper/2503.21321/) (2025)
- [A multi-view contrastive learning framework for spatial embeddings in risk modelling](https://mlsanity.com/paper/2511.17954/) (2025)
- [Revealing Geography-Driven Signals in Zone-Level Claim Frequency Models: An Empirical Study using Environmental and Visual Predictors](https://mlsanity.com/paper/2604.21893/) (2026)
- [Is TabPFN the Silver Bullet for Insurance Pricing?](https://mlsanity.com/paper/2605.22892/) (2026)

## Abstract (arXiv)

Insurers usually turn to generalized linear models for modeling claim frequency and severity data. Due to their success in other fields, machine learning techniques are gaining popularity within the actuarial toolbox. Our paper contributes to the literature on frequency-severity insurance pricing with machine learning via deep learning structures. We present a benchmark study on four insurance data sets with frequency and severity targets in the presence of multiple types of input features. We compare in detail the performance of: a generalized linear model on binned input data, a gradient-boosted tree model, a feed-forward neural network (FFNN), and the combined actuarial neural network (CANN). The CANNs combine a baseline prediction established with a GLM and GBM, respectively, with a neural network correction. We explain the data preprocessing steps with specific focus on the multiple types of input features typically present in tabular insurance data sets, such as postal codes, numeric and categorical covariates. Autoencoders are used to embed the categorical variables into the neural network, and we explore their potential advantages in a frequency-severity setting. Model performance is evaluated not only on out-of-sample deviance but also using statistical and calibration performance criteria and managerial tools to get more nuanced insights. Finally, we construct global surrogate models for the neural nets' frequency and severity models. These surrogates enable the translation of the essential insights captured by the FFNNs or CANNs to GLMs. As such, a technical tariff table results that can easily be deployed in practice.