Multicausal transport: barycenters and dynamic matching
Beatrice Acciaio, Daniel Kršek, Gudmund Pammer
TL;DR
The paper introduces multicausal transport as a multimarginal extension of causal transport for filtered processes and develops a corresponding theory of causal and bicausal barycenters within the adapted Wasserstein framework. It proves existence and duality results for the primal multicausal OT problem and its barycenter variants, and establishes a deep connection between bicausal barycenters and multicausal OT via a multimarginal reformulation. A dynamic matching application is then analyzed, showing that equilibria exist when agent types evolve over time and contracts are allocated through a causal barycenter mechanism. Overall, the work provides a rigorous bridge between dynamic transport, averaging of stochastic dynamics, and equilibrium formation in time-evolving markets, with potential implications for robust pricing, hedging, and dynamic contract design.
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.