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Preprints, Working Papers, ... Year : 2024

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

Abstract

We propose a discrete time formulation of the semi martingale optimal transport problem based 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 Föllmer 2022 and Backhoff-Veraguas and Unterberger 2023.
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hal-04613721 , version 1 (17-06-2024)

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  • HAL Id : hal-04613721 , version 1

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Jean-David Benamou, Guillaume Chazareix, Grégoire Loeper. From entropic transport to martingale transport, and applications to model calibration. 2024. ⟨hal-04613721⟩
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