Non-crossing Neural Network Quantile Regression Estimation for Driving Data with Telematics
The state-of-the-art methodologies to estimate Value at Risk (VaR) and Conditional Tail Expectation (CTE) controlled by covariates are mainly based on quantile regression and do not consider explicit constraints to guarantee that non-crossing conditions across VaRs and their associated CTEs always hold. We implement a non-crossing neural network that: a) estimates VaRs and CTE simultaneously, b) is conditional on covariates and c) preserves the natural quantile level order. We implement a Non-Crossing Dual Neural Network, a deep learning model capable of handling driving data using a telematics dataset from 2015 for quantile levels 0.9, 0.925, 0.95, 0.975 and 0.99. Improvements compared to quantile regression using lineal optimization and CTE estimation of one quantile level at a time are discussed. We also conclude that our method improves a Monotone Composite Quantile Regression Neural Network approximation and that it can be implemented in many areas of risk analysis.