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arXiv · 2401.12748

Multicausal transport: barycenters and dynamic matching

Beatrice Acciaio·Daniel Kršek·Gudmund Pammer
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Abstract

We introduce a multivariate version of causal transport, which we name multicausal transport, involving several filtered processes among which causality constraints are imposed. Subsequently, we consider the barycenter problem for stochastic processes with respect to causal and bicausal optimal transport, and study its connection to specific multicausal transport problems. Attainment and duality of the aforementioned problems are provided. As an application, we study a matching problem in a dynamic setting where agent types evolve over time. We link this to a causal barycenter problem and thereby show existence of equilibria.

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BibTeXRIS

Beatrice Acciaio, Daniel Kršek, Gudmund Pammer. 2024-01-23. Multicausal transport: barycenters and dynamic matching. https://arxiv.org/abs/2401.12748

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