A super-replication theorem in Kabanov's model of transaction costs
type: Item
instance of: scholarly article
title: A super-replication theorem in Kabanov's model of transaction costs
zbMATH Open document ID: 1126.91024
author: Luciano Campi
author: Walter Schachermayer
published in: Finance and Stochastics
publication date: 2007-05-29T00:00:00Z
review text: The authors prove a general super-replication theorem for bid-ask processes that are not necessarily continuous. The notions of admissible predictable portfolio process and of a strictly consistent price system (SCPS) are developed. The main result states that if there exists an SCPS then the set of attainable contingent claims is Fatou-closed with respect to the order induced by the final solvency cone. This means that it is possible to pass from a sequence of portfolio processes that are uniformly bounded from below to a limiting portfolio process. A central tool is a generalized and parameterised version of Helly's theorem on pointwise convergence for sequences of functions of uniformly bounded variation.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 5158702
zbMATH Keywords: proportional transaction costs
zbMATH Keywords: foreign exchange markets
zbMATH Keywords: efficient friction
zbMATH Keywords: super-replication theorem
MaRDI profile type: Publication
full work available at URL: s00780-006-0022-4
OpenAlex ID: W2160042775
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DOI: 10.1007/S00780-006-0022-4
description: scientific article; zbMATH DE number 5158702