A super-replication theorem in Kabanov's model of transaction costs

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 c`adl`ag bid-ask process (t)t[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 closure 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 [11], Kabanov and Last [12] and Kabanov and Stricker [15]. R

• Type: Journal
• Year: 2006
• Where: FS
• Authors: Luciano Campi, Walter Schachermayer
• Keywords: Bid-ask Process, Foreign Exchange Markets, FS 2006, Proportional Transaction Costs