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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.11537 |
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| _version_ | 1866913393543217152 |
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| author | Benamou, Jean-David Chazareix, Guillaume Loeper, Grégoire |
| author_facet | Benamou, Jean-David Chazareix, Guillaume Loeper, Grégoire |
| contents | We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et al. 2022, using a multi-marginal extension of Sinkhorn algorithm as in Benamou, Carlier, and Nenna 2019; Carlier et al. 2017; Benamou et al. 2019. In the limit when the time step goes to zero we recover, as detailed in the companion paper Benamou et al. 2024, a semi-martingale process, solution to a semi-martingale optimal transport problem, with a cost function involving the so-called specific entropy introduced in Gantert 1991, see also F{ö}llmer 2022 and Backhoff-Veraguas and Unterberger 2023. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From entropic transport to martingale transport, and applications to model calibration Benamou, Jean-David Chazareix, Guillaume Loeper, Grégoire Optimization and Control We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et al. 2022, using a multi-marginal extension of Sinkhorn algorithm as in Benamou, Carlier, and Nenna 2019; Carlier et al. 2017; Benamou et al. 2019. In the limit when the time step goes to zero we recover, as detailed in the companion paper Benamou et al. 2024, a semi-martingale process, solution to a semi-martingale optimal transport problem, with a cost function involving the so-called specific entropy introduced in Gantert 1991, see also F{ö}llmer 2022 and Backhoff-Veraguas and Unterberger 2023. |
| title | From entropic transport to martingale transport, and applications to model calibration |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.11537 |