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

Abstract

For calculating non-life insurance premiums, actuaries traditionally rely on separate severity and frequency models using covariates to explain the claims loss exposure. In this paper, we focus on the claim severity. First, we build two reference models, a generalized linear model and a generalized additive model, relying on a log-normal distribution of the severity and including the most significant factors. Thereby, we relate the continuous variables to the response in a nonlinear way. In the second step, we tune two random forest models, one for the claim severity and one for the log-transformed claim severity, where the latter requires a transformation of the predicted results. We compare the prediction performance of the different models using the relative error, the root mean squared error and the goodness-of-lift statistics in combination with goodness-of-fit statistics. In our application, we rely on a dataset of a Swiss collision insurance portfolio covering the loss exposure of the period from 2011 to 2015, and including observations from 81 309 settled claims with a total amount of CHF 184 mio. In the analysis, we use the data from 2011 to 2014 for training and from 2015 for testing. Our results indicate that the use of a log-normal transformation of the severity is not leading to performance gains with random forests. However, random forests with a log-normal transformation are the favorite choice for explaining right-skewed claims. Finally, when considering all indicators, we conclude that the generalized additive model has the best overall performance.

Equalization Reserves for Reinsurance and Non-Life Undertakings in Switzerland

“…Nevertheless, we use the same approach for both. We apply a popular approach, described in the literature, for example, by Staudt and Wagner (2021). In a first step, we define the GAM model by selecting the explanatory variables, having the highest impact on the equalization reserves.…”

“…Our goal is to link the response variable, equalization reserves, with the explanatory variables, presented in Table 4. We utilize a common approach, described for example by Staudt and Wagner (2021) to obtain the optimal GAM model: the best performance of variously defined models determines the best GAM model. The start is a GAM model having only one explanatory variable: each of the 12 available possible explanatory variables defines its own GAM model and the corresponding AIC value captures its performance.…”

“…Having determined the GAM Select , we look for optimal categorization of the significant explanatory variables, using evolutionary trees according to Staudt and Wagner (2021). Grubinger et al (2014) explain the optimal classification and regression trees in R: a recursive partitioning by choosing splits that maximize the homogeneity at the next step.…”

Gestion du risque et introduction aux assurances

“…16. L'illustration montre l'effet de l'âge du conducteur principal sur la sévérité des sinistres dans une assurance casco et se base sur les données d'un assureur suisse (Staudt et Wagner, 2021)…”

Special Issue “Risks: Feature Papers 2021”

“…Staudt and Wagner (2021)'s model claim severity by different random forest models and compare their performance. The results in the car insurance market are illustrated Candelon et al (2021).…”