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Explicit characterization of the super-replication strategy in financial markets with partial transaction costs

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Author Info
Imen Bentahar
Bruno Bouchard
Abstract

We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi (2000) except that some of the assets can be exchanged freely, i.e. without paying transaction costs. This is the so-called non-effcient friction case. To our knowledge, this is the first time that such a model is considered in a continuous time setting. In this context, we generalize the result of the above paper and prove that the super-replication price is given by the cost of the cheapest hedging strategy in which the number of non-freely exchangeable assets is kept constant over time.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-053.

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Length: 36 pages
Date of creation: Oct 2005
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Handle: RePEc:hum:wpaper:sfb649dp2005-053

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Keywords: Transaction costs hedging options viscosity solutions

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming

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  1. Szymon Borak & Kai Detlefsen & Wolfgang Härdle, 2005. "FFT Based Option Pricing," SFB 649 Discussion Papers SFB649DP2005-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Mountford, A. & Uhlig, H., 2002. "What are the effects of fiscal policy shocks?," Discussion Paper 31, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  3. Ralf Brüggemann & Carsten Trenkler, 2005. "Are Eastern European Countries Catching Up? Time Series Evidence for Czech Republic, Hungary, and Poland," SFB 649 Discussion Papers SFB649DP2005-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  4. Eun-Kyung Lee & Dianne Cook & Sigbert Klinke & Thomas Lumley, 2005. "Projection Pursuit for Exploratory Supervised Classification," SFB 649 Discussion Papers SFB649DP2005-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  5. Silke Anger, 2005. "Working Time as an Investment? : The Effects of Unpaid Overtime on Wages, Promotions, and Layoffs," Discussion Papers of DIW Berlin 535, DIW Berlin, German Institute for Economic Research. [Downloadable!]
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  6. Sigbert Klinke & Uwe Ziegenhagen & Yuval Guri, 2005. "Yxilon – a Modular Open-Source Statistical Programming Language," SFB 649 Discussion Papers SFB649DP2005-018, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  7. Enzo Giacomini & Wolfgang Härdle, 2005. "Value-at-Risk Calculations with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2005-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. Oliver Blaskowitz & Helmut Herwartz & Gonzalo de Cadenas Santiago, 2005. "Modeling the FIBOR/EURIBOR Swap Term Structure: An Empirical Approach," SFB 649 Discussion Papers SFB649DP2005-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  9. Dirk Krueger & Harald Uhlig, 2005. "Competitive Risk Sharing Contracts with One-Sided Commitment," CFS Working Paper Series 2005/07, Center for Financial Studies. [Downloadable!]
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  10. Harald Uhlig & Fiorella De Fiore, 2005. "Bank Finance versus Bond Finance: What Explains the Differences Between US and Europe?," 2005 Meeting Papers 618, Society for Economic Dynamics. [Downloadable!]
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  11. Szymon Borak & Matthias Fengler & Wolfgang Härdle, 2005. "DSFM fitting of Implied Volatility Surfaces," SFB 649 Discussion Papers SFB649DP2005-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  12. Alexander Schied & Ching-Tang Wu, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers SFB649DP2005-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Sep 2005. [Downloadable!]
  13. Yasemin Boztug & Lutz Hildebrandt, 2005. "A Market Basket Analysis Conducted with a Multivariate Logit Model," SFB 649 Discussion Papers SFB649DP2005-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  14. Michael C. Burda & Michael Kvasnicka, 2006. "Zeitarbeit in Deutschland: Trends und Perspektiven," Perspektiven der Wirtschaftspolitik, Blackwell Publishing, vol. 7(2), pages 195-225, 05. [Downloadable!] (restricted)
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  15. Ronald Bachmann, 2005. "Skill mismatch in equilibrium unemployment," SFB 649 Discussion Papers SFB649DP2005-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2005. [Downloadable!]
  16. Astrid Matthey, 2005. "Getting Used to Risks: Reference Dependence and Risk Inclusion," SFB 649 Discussion Papers SFB649DP2005-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  17. Bartosz Mackowiak & Mirko Wiederholt, 2004. "Optimal Sticky Prices under Rational Inattention," SFB 649 Discussion Papers SFB649DP2005-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Jul 2005. [Downloadable!]
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  18. Schabert, Andreas & Stoltenberg, Christian, 2005. "Money Demand and Macroeconomic Stability Revisited," CEPR Discussion Papers 4974, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  19. Ronald Bachmann, 2005. "Labour Market Dynamics in Germany: Hirings, Separations, and Job-to-Job Transitions over the Business Cycle," SFB 649 Discussion Papers SFB649DP2005-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  20. Almuth Scholl & Harald Uhlig, 2005. "New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates," SFB 649 Discussion Papers SFB649DP2005-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  21. Radosveta Ivanova-Stenzel & Dorothea Kübler, 2005. "Courtesy and Idleness: Gender Differences in Team Work and Team Competition," SFB 649 Discussion Papers SFB649DP2005-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  22. Alexander Schied, 2005. "Optimal Investments for Risk- and Ambiguity-Averse Preferences: A Duality Approach," SFB 649 Discussion Papers SFB649DP2005-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006. [Downloadable!]
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  23. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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