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Machine Learning Architectures for Price Formation Models

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Abstract

Here, we study machine learning (ML) architectures to solve a mean-field games (MFGs) system arising in price formation models. We formulate a training process that relies on a min–max characterization of the optimal control and price variables. Our main theoretical contribution is the development of a posteriori estimates as a tool to evaluate the convergence of the training process. We illustrate our results with numerical experiments for linear dynamics and both quadratic and non-quadratic models.

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Acknowledgements

This work is partially supported by Beijing International Center for Mathematical Research, the Elite Program of Computational and Applied Mathematics for PhD Candidates of Peking University, NSFC Grant 91430215, NSF Grants DMS-1522615 and DMS-1819157. Publisher Copyright: © 2020 Global Science Press. All rights reserved.

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The authors were partially supported by King Abdullah University of Science and Technology.

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Authors and Affiliations

  1. CEMSE Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    Diogo Gomes & Julian Gutierrez

  2. New York University Shanghai (NYU Shanghai), Shanghai, 200122, China

    Mathieu Laurière

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  1. Diogo Gomes
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  2. Julian Gutierrez
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Correspondence to Julian Gutierrez.

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The authors were partially supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2021-4674.

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Gomes, D., Gutierrez, J. & Laurière, M. Machine Learning Architectures for Price Formation Models. Appl Math Optim 88, 23 (2023). https://doi.org/10.1007/s00245-023-10002-8

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