Estimating Confidence Regions for Distortion Risk Measures and Their Gradients

This article constructs confidence regions (CRs) of distortion risk measures and their gradients at different risk levels based on replicate samples obtained from finite-horizon simulations. The CRs are constructed by batching and sectioning methods which partition the sample into nonoverlapping batches. Preliminary numerical results show that the estimated coverage rates of the CRs constructed are close to the nominal values.