Paper: arXiv 2310.12671

Authors: Freek Holvoet, Katrien Antonio, Roel Henckaerts

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a comprehensive, empirical benchmark study comparing traditional GLMs, tree-based models, and combined actuarial neural networks (CANN) across four real-world insurance datasets. It provides exceptional practical value by addressing data preprocessing, autoencoder embeddings for categorical features, out-of-sample calibration, and surrogate modeling to build interpretable technical tariffs.

Research Flowchart

  flowchart TD
    A["Research Goal: Benchmark DL/ML vs GLM<br/>for Frequency-Severity Insurance Pricing"] --> B["Data & Preprocessing:<br/>4 Insurance Datasets<br/><i>(Autoencoders for Categorical Embeddings)</i>"]
    
    B --> C["Model Training & Combination:<br/>• GLM & GBM<br/>• Feed-Forward Neural Nets (FFNN)<br/>• CANN (GLM/GBM + NN Correction)"]
    
    C --> D["Comprehensive Evaluation:<br/>Deviance, Statistical/Calibration Metrics,<br/>& Managerial Tools"]
    
    D --> E["Global Surrogate Models:<br/>Extract FFNN/CANN insights into GLMs"]
    
    E --> F["Key Outcome:<br/>Interpretable Technical Tariff Table<br/>for Practical Deployment"]