Computation of optimal transport and related hedging problems via penalization and neural networks
This work provides a general method for solving complex optimization problems in finance and machine learning, though it appears incremental as it builds on existing penalization and neural network techniques.
The paper tackles the computation of optimal transport and related hedging problems by introducing a penalization approach in the dual formulation, which is then solved using neural networks, demonstrating effectiveness across various numerical examples including portfolio optimization and generative adversarial networks.
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.