A Machine Learning Approach to Portfolio Pricing and Risk Management for High-Dimensional Problems
Swiss Finance Institute Research Paper No. 20-28
Mathematical Finance, forthcoming
45 Pages Posted: 2 May 2020 Last revised: 1 Apr 2022
Date Written: April 28, 2020
Abstract
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 leastsquares Monte Carlo.
Keywords: Solvency capital; dimensionality reduction; neural networks; nested Monte Carlo; replicating portfolios.
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