We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an effective low-dimensional representation, overcoming the curse...

We use machine learning methods to predict stock return volatility. Our out-of-sample prediction of realised volatility for a large cross-section of US stocks over the sample period from 1992 to 2016 is on average 44.1% against the actual realised volatility of 43.8% with an R2 being as high as...