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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

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Article accepté pour publication ou publié
External document link
http://projecteuclid.org/euclid.aoap/1019487506
Date
2000
Journal name
The Annals of Applied Probability
Volume
10
Number
3
Publisher
Institute of Mathematical Statistics
Pages
685-708
Publication identifier
Metadata
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Author(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Touzi, Nizar
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / Keywords
viscosity solutions; dynamic programming; hedging options; Transaction costs
JEL
G13 - Contingent Pricing; Futures Pricing
G11 - Portfolio Choice; Investment Decisions
D53 - Financial Markets