A Machine Learning Approach to Portfolio Pricing and Risk Management for High-Dimensional Problems
44 Pages Posted: 2 May 2020 Last revised: 22 May 2020
Date Written: April 28, 2020
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.
Keywords: Solvency capital; dimensionality reduction; neural networks; nested Monte Carlo; replicating portfolios.
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