A super-replication theorem in Kabanov’s model of transaction costs View Full Text


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Article Info

DATE

2006-11-04

AUTHORS

Luciano Campi, Walter Schachermayer

ABSTRACT

We prove a general version of the super-replication theorem, which applies to Kabanov’s model of foreign exchange markets under proportional transaction costs. The market is described by a matrix-valued càdlàg bid-ask process \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\Pi_t)_{t\in [0,T]}$$\end{document} evolving in continuous time. We propose a new definition of admissible portfolio processes as predictable (not necessarily right- or left- continuous) processes of finite variation related to the bid-ask process by economically meaningful relations. Under the assumption of existence of a strictly consistent price system (SCPS), we prove a closedness property for the set of attainable vector-valued contingent claims. We then obtain the super-replication theorem as a consequence of that property, thus generalizing to possibly discontinuous bid-ask processes analogous results obtained by Kabanov (Financ. Stoch. 3, 237–248, 1999), Kabanov and Last (Math. Financ. 12, 63–70, 2002) and Kabanov and Stricker (Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, pp 125–136, 2002). Rásonyi’s counter-example (Lecture Notes in Mathematics 1832, 394–398, 2003) served as an important motivation for our approach. More... »

PAGES

579-596

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00780-006-0022-4

DOI

http://dx.doi.org/10.1007/s00780-006-0022-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040347963


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