# From entropic transport to martingale transport, and applications to model calibration

arXiv: https://arxiv.org/abs/2406.11537 · HTML: https://mlsanity.com/paper/2406.11537/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysis](https://mlsanity.com/paper/2510.11829/) (2025)

## Abstract (arXiv)

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"ollmer 2022 and Backhoff-Veraguas and Unterberger 2023.