Please use this identifier to cite or link to this item:
Title: On the stability of the martingale optimal transport problem: a set-valued map approach
Authors: Neufeld, Ariel
Sester, Julian
Keywords: Science::Mathematics
Issue Date: 2021
Source: 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-.
Journal: Statistics and Probability Letters
Abstract: 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.
ISSN: 0167-7152
DOI: 10.1016/j.spl.2021.109131
Schools: School of Physical and Mathematical Sciences 
Rights: © 2021 Published by Elsevier B.V. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

Citations 50

Updated on Nov 25, 2023

Web of ScienceTM
Citations 50

Updated on Oct 31, 2023

Page view(s)

Updated on Nov 28, 2023

Google ScholarTM




Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.