Stability of martingale optimal transport and weak optimal transport
By Julio Backhoff-Veraguas, Gudmund Pammer. The Annals of Applied Probability, 2019
63 citations recorded by the source corpus.
Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $\pi_1, \pi_2, \ldots$ converges weakly to a transport plan $\pi$, then $\pi$ is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for the martingale transport problem. This question seems particularly pressing since martingale transport is motivated by robust finance where data is naturally noisy. On a technical level, stability in the martingale case appears more intricate than for classical transport since optimal transport plans $\pi$ are not characterized by a `monotonicity'-property of their support. In this paper we give a positive answer and establish stability of the martingale transport problem. As a particular case, this recovers the stability of the left curtain coupling established by Juillet. An important auxiliary tool is an unconventional topology which takes the temporal structure of martingales into account. Our techniques also apply to the the weak transport problem introduced by Gozlan, Roberto, Samson and Tetali.
Subfields: Applied Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/79c51877d1d8e70585e8a84687731dd45e82e068
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Daniel Bartl
- Mathias Beiglbock
- Julio Backhoff-Veraguas
- Martin Huesmann
- Gudmund Pammer
- Sigrid Kallblad
- Manu Eder
- Nizar Touzi
In Statistics and Probability
- Mathias Beiglbock
- Daniel Bartl
- Gudmund Pammer
- Julio Backhoff-Veraguas
- Sigrid Kallblad
- Martin Huesmann
Citations in the corpus
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- All adapted topologies are equal (2019, background): “Specifically, in [8, 9] the two-step version of Lemma 1.”