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

Yves Staudt and Joël Wagner
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Yves Staudt: Department Alpine Region Development, Institute for Tourism and Leisure, University of Applied Sciences of the Grisons, Comercialstrasse 19, 7000 Chur, Switzerland
Joël Wagner: Department of Actuarial Science, Faculty of Business and Economics (HEC Lausanne), University of Lausanne, Extranef, 1015 Lausanne, Switzerland

Risks, 2021, vol. 9, issue 3, 1-28

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.

Keywords: regression model; data-driven binning; random forest; performance analysis; severity modeling (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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