Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs
Bouchard, Bruno; Touzi, Nizar (2000), Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs, The Annals of Applied Probability, 10, 3, p. 685-708. http://dx.doi.org/10.1214/aoap/1019487506
TypeArticle accepté pour publication ou publié
External document linkhttp://projecteuclid.org/euclid.aoap/1019487506
Journal nameThe Annals of Applied Probability
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Abstract (EN)We consider a multivariate financial market with transaction 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.
Subjects / Keywordsviscosity solutions; dynamic programming; hedging options; Transaction costs
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