Deep Stochastic Optimization in Finance

TL;DR

This paper introduces a novel computational technique combining Empirical Risk Minimization and neural networks for high-dimensional stochastic optimization in finance, demonstrating its effectiveness through option pricing and hedging applications.

Contribution

It presents a new approach leveraging ERM and neural networks, supported by open source tools, to efficiently solve complex high-dimensional financial problems.

Findings

Effective in high-dimensional option pricing

Requires large training data or market simulations

Highlights potential difficulties in specific applications

Abstract

This paper outlines, and through stylized examples evaluates a novel and highly effective computational technique in quantitative finance. Empirical Risk Minimization (ERM) and neural networks are key to this approach. Powerful open source optimization libraries allow for efficient implementations of this algorithm making it viable in high-dimensional structures. The free-boundary problems related to American and Bermudan options showcase both the power and the potential difficulties that specific applications may face. The impact of the size of the training data is studied in a simplified Merton type problem. The classical option hedging problem exemplifies the need of market generators or large number of simulations.