A data driven binning strategy for the construction of insurance tariff classes

Abstract

We present a fully data driven strategy to incorporate continuous risk factors and geographical information in an insurance tariff. A framework is developed that aligns flexibility with the practical requirements of an insurance company, its policyholders and the regulator. Our strategy is illustrated with an example from property and casualty (P&C) insurance, namely a motor insurance case study. We start by fitting generalized additive models (GAMs) to the number of reported claims and their corresponding severity. These models allow for flexible statistical modeling in the presence of different types of risk factors: categorical, continuous and spatial risk factors. The goal is to bin the continuous and spatial risk factors such that categorical risk factors result which capture the effect of the covariate on the response in an accurate way, while being easy to use in a generalized linear model (GLM). This is in line with the requirement of an insurance company to construct a practical and interpretable tariff that can be explained easily to stakeholders. We propose to bin the spatial risk factor using Fisher's natural breaks algorithm and the continuous risk factors using evolutionary trees. GLMs are fitted to the claims data with the resulting categorical risk factors. We find that the resulting GLMs approximate the original GAMs closely, and lead to a very similar premium structure.

Assessing the Performance of Random Forests for Modeling Claim Severity in Collision Car Insurance

“…We extend this step by applying goodness-of-lift statistics (GOL), see Denuit et al (2019). Two reference models are derived, an optimal GAM and a GLM using data-driven binning for continuous covariates following the techniques of Henckaerts et al (2018). Because the GLM with categorical variables is still the favorite model setup in many insurance companies, it is important for us to measure the performance of the data-driven binning method along GOF and GOL.…”

“…Machine learning methods are applied in the context of ratemaking (Dalkilic et al 2009;Huang and Meng 2019;Lowe and Pryor 1996;Pelessoni and Picech 1998;Richman 2018), fraud detection (Li et al 2018;Wang and Xu 2018), extreme value theory (Velthoen et al 2021), forecasting (Perla et al 2020), and in the explanation of the lapse behavior of customers (Guelman et al 2012;Hu et al 2020;Staudt and Wagner 2020), among others. While such models are used to select relevant risk factors and automate the creation of categories for continuous variables (Dougherty et al 1995;Henckaerts et al 2018), full-pricing applications are scarce, see, e.g., Guelman (2012) and Henckaerts et al (2020). In claims modeling, most of the current academic research focuses on machine learning methods to develop claim frequency models (Denuit et al 2020;Ferrario et al 2018;Noll et al 2018;Schelldorfer and Wüthrich 2019;Wüthrich and Buser 2018) and much less attention is given to severity modeling (see, e.g., Dewi et al 2019;Staudt and Wagner 2019).…”

Machine Learning in P&C Insurance: A Review for Pricing and Reserving

“…Generalized additive models in insurance academia were first studied by Denuit and Lang (2004) and revisited with GAMLSS in Klein et al (2014). This model was also used in actuarial ratemaking by Henckaerts et al (2018), who employed generalized additive models to discover nonlinear relationships in continuous and spatial risk factors. Then, these flexible functions are binned into categorical variables and used as a variable in a GLM.…”

Defining Geographical Rating Territories in Auto Insurance Regulation by Spatially Constrained Clustering

“…Rate filing is an important aspect in auto insurance regulation of pricing. The purpose of rate filings is to ensure that insurance premiums offered by insurance companies are fair and exact Antonio and Beirlant (2018); Henckaerts et al (2018); Xie and Lawniczak (2018); Harrington (1991Harrington ( , 1984; Leadbetter et al (2008). Furthermore, within this process, insurance companies are required to demonstrate the appropriateness of methodologies used for pricing.…”

“…That is, territorial rate-making is determined using insureds' characteristics including both individual loss experience and residential information. For instance, in Henckaerts et al (2018), a data-driven strategy was presented by incorporating both continuous risk factors and territorial information in an auto insurance premium calculation. Since regulators have no access to such information for each individual insured and the loss experience is aggregated by regions, many of the existing clustering techniques used by insurance companies are no longer applicable to the insurance regulators.…”