A machine learning approach to portfolio pricing and risk management for high‐dimensional problems

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).