XGBoost is recognized as an algorithm with exceptional predictive capacity. Models for a binary response indicating the existence of accident claims versus no claims can be used to identify the determinants of traffic accidents. This study compared the relative performances of logistic regression and XGBoost approaches for predicting the existence of accident claims using telematics data. The dataset contained information from an insurance company about the individuals’ driving patterns—including total annual distance driven and percentage of total distance driven in urban areas. Our findings showed that logistic regression is a suitable model given its interpretability and good predictive capacity. XGBoost requires numerous model-tuning procedures to match the predictive performance of the logistic regression model and greater effort as regards to interpretation.

When estimating loss distributions in insurance, large and small losses are usually split because it is difficult to find a simple parametric model that fits all claim sizes. This approach involves determining the threshold level between large and small losses. In this article, a unified approach to the estimation of loss distributions is presented. We propose an estimator obtained by transforming the data set with a modification of the Champernowne cdf and then estimating the density of the transformed data by use of the classical kernel density estimator. We investigate the asymptotic bias and variance of the proposed estimator. In a simulation study, the proposed method shows a good performance. We also present two applications dealing with claims costs in insurance.

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed‐form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between GlueVaR, value‐at‐risk, and tail value‐at‐risk is explained. Tail subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in nonfinancial problems such as health, safety, environmental, or catastrophic risk management.