Laporta, A. G., Levantesi, S., & Petrella, L. (2023). Neural networks for quantile claim amount estimation: A quantile regression approach. Published online May 17, 2023, by Cambridge University Press.

Neural network-based models for conditional quantile estimation in non-life insurance can significantly impact profitability by providing better risk assessment and premium pricing strategies. 

The paper presents a study on the estimation of conditional quantiles of aggregate claim amounts for non-life insurance using a quantile regression framework with a neural network approach.

A Quantile Regression Neural Network (QRNN) is a hybrid method that was developed based on quantile regression (QR). It can model data with non-homogeneous variance and uses a neural network that can capture nonlinear patterns in the data.

The authors introduce two models: QRNN and the Quantile-CANN, which combines traditional quantile regression with a QRNN. These models are applied to a health insurance dataset, demonstrating improved performance compared to classical quantile regression. The estimated quantiles are then utilized to calculate a loaded premium, indicating that the proposed models offer enhanced risk differentiation.

Both models use a two-part structure - a logistic regression to estimate claim probability, and the QRNN/Quantile-CANN to model positive claim outcomes.

1. Quantile regression neural networks (QRNN), which have not been used before in actuarial sciences.

2. A new model called Quantile-CANN that combines traditional quantile regression with a QRNN.

The models are tested on a health insurance dataset and show better performance than classical quantile regression in terms of quantile loss

The neural network models exhibit better risk differentiation vs. quantile regression, allowing for better differentiation between good and bad risks and are a useful tool for high-dimensional nonlinear regression in insurance ratemaking.