Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs
AbstractWe 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.
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Bibliographic InfoPaper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/1533.
Date of creation: 2000
Date of revision:
Publication status: Published in Annals of Applied Probability, 2000, Vol. 10, no. 3. pp. 685-708.Length: 23 pages
viscosity solutions; dynamic programming; hedging options; Transaction costs;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
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- Campi, Luciano & Schachermayer, Walter, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Economics Papers from University Paris Dauphine 123456789/5455, Paris Dauphine University.
- Bruno Bouchard, 2005. "No-arbitrage in discrete-time markets with proportional transaction costs and general information structure," Papers math/0501045, arXiv.org.
- Bentahar, Imen & Bouchard, Bruno, 2007. "Explicit characterization of the super-replication strategy in financial markets with partial transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 655-672, May.
- Tomasz R. Bielecki & Igor Cialenco & Rodrigo Rodriguez, 2012. "No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs," Papers 1205.6254, arXiv.org, revised Jun 2013.
- Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org.
- Bruno Bouchard & Ngoc-Minh Dang, 2013. "Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation," Finance and Stochastics, Springer, vol. 17(1), pages 31-72, January.
- Bouchard, Bruno, 2002. "Stochastic targets with mixed diffusion processes and viscosity solutions," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 273-302, October.
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