  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{\"o}llmer 2022 and Backhoff-Veraguas and Unterberger 2023.
