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

Insurers usually turn to generalized linear models for modelling 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). Our 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. 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.

Model-Agnostic Interpretable and Data-driven suRRogates suited for highly regulated industries

Highly regulated industries, like banking and insurance, ask for transparent decision-making algorithms. At the same time, competitive markets push for sophisticated black box models. We therefore present a procedure to develop a Model-Agnostic Interpretable Data-driven suRRogate, suited for structured tabular data. Insights are extracted from a black box via partial dependence effects. These are used to group feature values, resulting in a segmentation of the feature space with automatic feature selection. A transparent generalized linear model (GLM) is fit to the features in categorical format and their relevant interactions. We demonstrate our R package maidrr with a case study on general insurance claim frequency modeling for six public datasets. Our maidrr GLM closely approximates a gradient boosting machine (GBM) and outperforms both a linear and tree surrogate as benchmarks.

Boosting insights in insurance tariff plans with tree-based machine learning

Pricing actuaries typically stay within the framework of generalized linear models (GLMs). With the upswing of data analytics, our study puts focus on machine learning to develop full tariff plans built from both the frequency and severity of claims. We adapt the loss functions used in the algorithms such that the specific characteristics of insurance data are carefully incorporated: highly unbalanced count data with excess zeros and varying exposure on the frequency side combined with scarce, but potentially long-tailed data on the severity side. A key requirement is the need for transparent and interpretable pricing models which are easily explainable to all stakeholders. We therefore focus on machine learning with decision trees: starting from simple regression trees, we work towards more advanced ensembles such as random forests and boosted trees. We show how to choose the optimal tuning parameters for these models in an elaborate cross-validation scheme, we present visualization tools to obtain insights from the resulting models and the economic value of these new modeling approaches is evaluated. Boosted trees outperform the classical GLMs, allowing the insurer to form profitable portfolios and to guard against potential adverse selection risks.