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A closed-form solution to the problem of super-replication under transaction costs

Listed author(s):
  • HuyËn Pham


    (Equipe d'Analyse et de MathÊmatiques AppliquÊes, UniversitÊ Marne-la-VallÊe, F-77454 Marne-la-VallÊe Cedex 2, France and CREST)

  • Nizar Touzi


    (CEREMADE, UniversitÊ Paris Dauphine, F-75775 Paris Cedex, France and CREST Manuscript)

  • Jaksa Cvitanic


    (Department of Statistics, Columbia University, New York, NY 10027, USA)

We study the problem of finding the minimal price needed to dominate European-type contingent claims under proportional transaction costs in a continuous-time diffusion model. The result we prove has already been known in special cases - the minimal super-replicating strategy is the least expensive buy-and-hold strategy. Our contribution consists in showing that this result remains valid for general path-independent claims, and in providing a shorter and more intuitive, financial mathematics-type proof. It is based on a previously known representation of the minimal price as a supremum of the prices in corresponding shadow markets, and on a PDE (viscosity) characterization of that representation.

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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 3 (1999)
Issue (Month): 1 ()
Pages: 35-54

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Handle: RePEc:spr:finsto:v:3:y:1999:i:1:p:35-54
Note: received: May 1997; final version received: October 1997
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