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

HuyËn Pham (), Nizar Touzi () and Jaksa Cvitanic ()
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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

Finance and Stochastics, 1999, vol. 3, issue 1, 35-54

Abstract: 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.

Keywords: Transaction costs; super-replicating strategies; viscosity solutions (search for similar items in EconPapers)
JEL-codes: G11 G13 (search for similar items in EconPapers)
Date: 1998-11-17
Note: received: May 1997; final version received: October 1997
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Citations: View citations in EconPapers (9)

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