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

See all articles by Lucio Fernandez Arjona

Lucio Fernandez Arjona

Zurich Insurance Group

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

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.

Suggested Citation

Fernandez Arjona, Lucio and Filipovic, Damir, A Machine Learning Approach to Portfolio Pricing and Risk Management for High-Dimensional Problems (April 28, 2020). Swiss Finance Institute Research Paper No. 20-28, Mathematical Finance, forthcoming, Available at SSRN: https://ssrn.com/abstract=3588376 or http://dx.doi.org/10.2139/ssrn.3588376

Lucio Fernandez Arjona

Zurich Insurance Group ( email )

P.O. Box
Mythenquai 2
Zürich, 8022
Switzerland

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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