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Published in: Mathematics and Financial Economics 4/2014

01-09-2014

The super-replication theorem under proportional transaction costs revisited

Author: Walter Schachermayer

Published in: Mathematics and Financial Economics | Issue 4/2014

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Abstract

We consider a financial market with one riskless and one risky asset. The super-replication theorem states that there is no duality gap in the problem of super-replicating a contingent claim under transaction costs and the associated dual problem. We give two versions of this theorem. The first theorem relates a numéraire-based admissibility condition in the primal problem to the notion of a local martingale in the dual problem. The second theorem relates a numéraire-free admissibility condition in the primal problem to the notion of a uniformly integrable martingale in the dual problem.

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Metadata
Title
The super-replication theorem under proportional transaction costs revisited
Author
Walter Schachermayer
Publication date
01-09-2014
Publisher
Springer Berlin Heidelberg
Published in
Mathematics and Financial Economics / Issue 4/2014
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-014-0129-x

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