## Computation of Optimal Transport and Related Hedging Problems via Penalization and Neural Networks

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2021
Journal article
Published
##### Published in
Applied Mathematics & Optimization ; 83 (2021), 2. - pp. 639-667. - Springer. - ISSN 0095-4616. - eISSN 1432-0606
##### 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.
510 Mathematics
##### Cite This
ISO 690ECKSTEIN, Stephan, Michael KUPPER, 2021. Computation of Optimal Transport and Related Hedging Problems via Penalization and Neural Networks. In: Applied Mathematics & Optimization. Springer. 83(2), pp. 639-667. ISSN 0095-4616. eISSN 1432-0606. Available under: doi: 10.1007/s00245-019-09558-1
BibTex
@article{Eckstein2021Compu-53512,
year={2021},
doi={10.1007/s00245-019-09558-1},
title={Computation of Optimal Transport and Related Hedging Problems via Penalization and Neural Networks},
number={2},
volume={83},
issn={0095-4616},
journal={Applied Mathematics & Optimization},
pages={639--667},
author={Eckstein, Stephan and Kupper, Michael}
}

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Yes
Yes