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August 2000 Explicit solution to the multivariate super-replication problem under transaction costs
Bruno Bouchard, Nizar Touzi
Ann. Appl. Probab. 10(3): 685-708 (August 2000). DOI: 10.1214/aoap/1019487506


We consider a multivariate .nancial market withtransaction costs as in Kabanov. We study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. We prove that the value of this stochastic control problem is given by the cost of the cheapest buy-and-hold strategy. This is an extension of the already known result in the one-dimensional case. An important feature of our analysis is that we do not make use of the dual formulation of the problem, as in the previous literature.


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Bruno Bouchard. Nizar Touzi. "Explicit solution to the multivariate super-replication problem under transaction costs." Ann. Appl. Probab. 10 (3) 685 - 708, August 2000.


Published: August 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1083.91510
MathSciNet: MR1789976
Digital Object Identifier: 10.1214/aoap/1019487506

Primary: 60H30 , 90A09 , 93E20
Secondary: 60G44 , 90A16

Keywords: dynamic programming , hedging options , Transaction costs , viscosity solutions

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 3 • August 2000
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