Dynamic characterization of barycentric optimal transport problems and their martingale relaxation

2025/11/26 by Guo, Ivan, Nilsson, Severin, Wiesel, Johannes
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2511.21287

Abstract

We extend the Benamou-Brenier formula from classical optimal transport to weak optimal transport and show that the barycentric optimal transport problem studied by Gozlan and Juillet has a dynamic analogue. We also investigate a martingale relaxation of this problem, and relate it to the martingale Benamou-Brenier formula of Backhoff-Veraguas, Beiglböck, Huesmann and Källblad.

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Related

• A Benamou-Brenier formulation of martingale optimal transport
• Existence of Bass martingales and the martingale Benamou-Brenier problem in ℝ^d
• The Fundamental Theorem of Weak Optimal Transport
• A Benamou-Brenier formulation for the multi-marginal optimal transport problem with infimal convolution cost
• Martingale Benamou--Brenier: a probabilistic perspective