On the stability of the martingale optimal transport problem: a set-valued map approach

On the stability of the martingale optimal transport problem: a set-valued map approach

Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer (2019) and Wiesel (2019). We present a new perspective of this result using the theory of set-valued maps. In particular, using results f...

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Main Authors: Neufeld, Ariel, Sester, Julian
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Science::Mathematics
Martingale Optimal Transport
Stability
Online Access:https://hdl.handle.net/10356/159941
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1599412022-07-06T02:50:27Z On the stability of the martingale optimal transport problem: a set-valued map approach Neufeld, Ariel Sester, Julian School of Physical and Mathematical Sciences Science::Mathematics Martingale Optimal Transport Stability Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer (2019) and Wiesel (2019). We present a new perspective of this result using the theory of set-valued maps. In particular, using results from Beiglböck et al. (2021), we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals. Moreover, we establish compactness of the set of optimizers as well as upper hemicontinuity of the optimizers w.r.t. the marginals. Nanyang Technological University Financial support by the Nanyang Assistant Professorship, Singapore Grant (NAP Grant) Machine Learning based Algorithms in Finance and Insurance is gratefully acknowledged. 2022-07-06T02:50:27Z 2022-07-06T02:50:27Z 2021 Journal Article Neufeld, A. & Sester, J. (2021). On the stability of the martingale optimal transport problem: a set-valued map approach. Statistics and Probability Letters, 176, 109131-. https://dx.doi.org/10.1016/j.spl.2021.109131 0167-7152 https://hdl.handle.net/10356/159941 10.1016/j.spl.2021.109131 2-s2.0-85107112369 176 109131 en Statistics and Probability Letters © 2021 Published by Elsevier B.V. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Martingale Optimal Transport
Stability
spellingShingle Science::Mathematics
Martingale Optimal Transport
Stability
Neufeld, Ariel
Sester, Julian
On the stability of the martingale optimal transport problem: a set-valued map approach
description Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer (2019) and Wiesel (2019). We present a new perspective of this result using the theory of set-valued maps. In particular, using results from Beiglböck et al. (2021), we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals. Moreover, we establish compactness of the set of optimizers as well as upper hemicontinuity of the optimizers w.r.t. the marginals.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Neufeld, Ariel
Sester, Julian
format Article
author Neufeld, Ariel
Sester, Julian
author_sort Neufeld, Ariel
title On the stability of the martingale optimal transport problem: a set-valued map approach
title_short On the stability of the martingale optimal transport problem: a set-valued map approach
title_full On the stability of the martingale optimal transport problem: a set-valued map approach
title_fullStr On the stability of the martingale optimal transport problem: a set-valued map approach
title_full_unstemmed On the stability of the martingale optimal transport problem: a set-valued map approach
title_sort on the stability of the martingale optimal transport problem: a set-valued map approach
publishDate 2022
url https://hdl.handle.net/10356/159941
_version_ 1738844886479667200

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