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Consistent Price Systems in Multiasset Markets

Maris, F.; Sayit, H.

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Authors

F. Maris

H. Sayit



Abstract

Let Xt be any d-dimensional continuous process that takes values in an open connected domain O in Rd. In this paper, we give equivalent formulations of the conditional full support CFS property of Xt in O.We use them to show that the CFS property of X in O implies the existence of a martingale M under an equivalent probability measure such that M lies in the > 0 neighborhood of Xt for any given under the supremum norm. The existence of such martingales, which are called consistent price systems CPSs, has relevance with absence of arbitrage and hedging problems in markets with proportional transaction costs as discussed in the recent paper by Guasoni et al. 2008, where the CFS property is introduced and shown sufficient for CPSs for processes with certain state space. The current paper extends the results in the work of Guasoni et al. 2008, to processes with more general state space.

Citation

Maris, F., & Sayit, H. (2012). Consistent Price Systems in Multiasset Markets. International journal of stochastic analysis, 2012, Article 687376. https://doi.org/10.1155/2012/687376

Journal Article Type Article
Acceptance Date Jul 9, 2012
Publication Date Jul 9, 2012
Deposit Date Apr 16, 2014
Publicly Available Date Sep 9, 2015
Journal International Journal of Stochastic Analysis
Print ISSN 2090-3332
Electronic ISSN 2090-3340
Publisher Hindawi
Peer Reviewed Peer Reviewed
Volume 2012
Article Number 687376
DOI https://doi.org/10.1155/2012/687376

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
© 2012 Florian Maris and Hasanjan Sayit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.




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