Computation of optimal transport and related hedging problems via penalization and neural networks

TL;DR

This paper introduces a neural network-based penalization method to solve complex optimal transport and hedging problems efficiently, demonstrating broad applicability and effectiveness across various financial and generative modeling tasks.

Contribution

The paper proposes a novel neural network approach using penalization in the dual formulation to solve multi-marginal and martingale optimal transport problems.

Findings

Effective in solving optimal transport problems

Applicable to portfolio optimization and GANs

Demonstrates broad versatility and accuracy

Abstract

This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, martingale optimal transport, portfolio optimization under uncertainty and generative adversarial networks that showcase the generality and effectiveness of the approach.