Quantile Regression Neural Network for Quantile Claim Amount Estimation

Quantile Regression to estimate the conditional quantile of the claim amount for car insurance policies has already been by Heras et al. (An application of two-stage quantile regression to insurance ratemaking. Scand. Actuar. J. 2018, 2018) [1] and others. In this paper, we explore two alternative approaches, the first involves Quantile Regression Neural Networks (QRNN), while the second is an extension of the Combined Actuarial Neural Network (CANN) by Schelldorfer and Wüthrich (Nesting classical actuarial models into neural networks. SSRN, 2019) [2] where we nest the Quantile Regression model into the structure of a neural network (Quantile-CANN). This technique captures additional information respect to the simple Quantile Regression, representing non linear relationship between the covariates and the dependent variable, and involving possible interactions between predictors. To compute the conditional quantile of the total claim amount for a generic car insurance policy, we adopt the two part model approach discussed by Heras et al. (An application of two-stage quantile regression to insurance ratemaking. Scand. Actuar. J. 2018, 2018) [1]. In a first step, we fit a logistic regression to estimate the probability of positive claim. Then, conditional on positive outcome, we use QRNN and Quantile-CANN to estimate the conditional quantile of the total claim amount. The simulation results show that QRNN and Quantile-CANN exhibit an overall better performance in terms of quantile loss function with respect to the classical Quantile Regression.