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Multicausal transport: barycenters and dynamic matching

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  • Beatrice Acciaio
  • Daniel Krv{s}ek
  • Gudmund Pammer

Abstract

We introduce a multivariate version of adapted 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 agents' types evolve over time. We link this to a causal barycenter problem and thereby show existence of equilibria.

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  • Beatrice Acciaio & Daniel Krv{s}ek & Gudmund Pammer, 2024. "Multicausal transport: barycenters and dynamic matching," Papers 2401.12748, arXiv.org.
    • Handle: RePEc:arx:papers:2401.12748
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    References listed on IDEAS

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    1. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    2. Pierre-André Chiappori & Bernard Salanié, 2016. "The Econometrics of Matching Models," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 832-861, September.
    3. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    4. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 443-464.
    5. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
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