  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 of
dimensionality common to function approximation in high-dimensional spaces. We
show results based on polynomial and neural network bases. Both offer superior
results to naive Monte Carlo methods and other existing methods like
least-squares Monte Carlo and replicating portfolios.
