
A super-replication theorem in Kabanov’s model of transaction costs
Campi, Luciano; Schachermayer, Walter (2006), A super-replication theorem in Kabanov’s model of transaction costs, Finance and Stochastics, 10, 4, p. 579-596. http://dx.doi.org/10.1007/s00780-006-0022-4
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Article accepté pour publication ou publiéDate
2006Journal name
Finance and StochasticsVolume
10Number
4Publisher
Springer
Pages
579-596
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Show full item recordAbstract (EN)
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 $$(\Pi_t)_{t\in [0,T]}$$ 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.Subjects / Keywords
Proportional transaction costs; Foreign exchange markets; Efficient friction; Super-replication theoremRelated items
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