Arabian Journal of Mathematics

, Volume 6, Issue 2, pp 65–73 | Cite as

On representations of the set of supermartingale measures and applications in discrete time

  • Abdelkarem Berkaoui
Open Access


We investigate some new results concerning the m-stability property. We show in particular under the martingale representation property with respect to a bounded martingale S that an m-stable set of probability measures is the set of supermartingale measures for a family of discrete integral processes with respect to S.

Mathematics Subject Classification

60G42 91B24 


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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, College of ScienceAl-Imam Mohammed Ibn Saud Islamic University (IMSIU)RiyadhSaudi Arabia

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