Boosting Insights in Insurance Tariff Plans with Tree-Based Machine Learning Methods

Abstract

Pricing actuaries typically operate within the framework of generalized linear models (GLMs). With the upswing of data analytics, our study puts focus on machine learning methods 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 risk selection.

Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing

“…The frequency-severity method, which involves separate consideration of frequency and severity (Anderson et al 2007;Henckaerts et al 2019) to calculate the indicated cost, is one of the two fundamental actuarial pricing processes. The cost calculations are achieved by multiplying the conditional expectation of severity with expected claim frequency.…”

“…The authors summed up that the generalized additive model was able to outperform the generalized linear model for non-log-linear components. Similarly, Lee and Antonio (2015) and Henckaerts et al (2019) compared the performance of GLM, GAM, bagging, random forest, and Gradient boosting (GB). When full tariff insurance plans were created, gradient boosting outperformed GLMs allowing the insurers to form profitable portfolios along with guarding them against any adverse risk selection.…”

An Acceptance Approach for Novel Technologies in Car Insurance

“…Risk assessment and price setting are the core activity of insurers. A myriad of different data mining and machine learning approaches have been proposed to predict car accidents and accident claims [27,28]. For instance, [29] explained how new information (the event of a serious road accident being detected, based on airbag deployment and impact sensor information, transmitting GPS co-ordinates to local authorities in an effort to reduce response times and get assistance to the crash scene more quickly) would impact the price setting for European insurers.…”

Predictive Claim Scores for Dynamic Multi-Product Risk Classification in Insurance

“…with N, S = L/N, and F = N/e the number of claims, the average claim severity, and the claim frequency, respectively (Antonio and Valdez, 2012;Henckaerts et al, 2020). While we can allow the claim frequencies and severities to interact, it is in general common practice to model these two components independently (see, e.g., Czado et al, 2012;Garrido et al, 2016).…”

“…The Gini index is defined as twice the distance between this Lorenz curve and the line of equality and thus represents a measure of inequality (Gini, 1912). More importantly, in the context of insurance rate making, the Lorenz curve and the corresponding Gini index can also be adopted as a measure of risk discrimination (see, e.g., Frees et al, 2014;Henckaerts et al, 2020). To find the Lorenz curve in practice, we can use the following three steps: (i) Construct the relativity R j = P A j /P B j for each policy j = 1, .…”