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. Our method learns the features necessary for an effective low-dimensional representation, overcoming the curse of dimensionality common to function approximation in high-dimensional spaces, and applies for a wide range of model distributions. We show numerical results based on polynomial and neural network bases applied to high-dimensional Gaussian models. In these examples, both bases offer superior results to naive Monte Carlo methods and regress-now least-squares Monte Carlo (LSMC).