On the Hedging of American Options in Discrete Time with Proportional Transaction Costs
Bruno Bouchard, Université Paris 6 and CREST, France
Emmanuel Teman, Université Paris 6, France
Abstract
In this note, we consider a general discrete time financial market
with proportional transaction costs as in Kabanov and Stricker
(2001), Kabanov et al. (2002), Kabanov et al. (2003) and
Schachermayer (2004). We provide a dual formulation for the set of
initial endowments which allow to super-hedge some American claim. We
show that this extends the result of Chalasani and Jha (2001) which
was obtained in a model with constant transaction costs and risky
assets which evolve on a finite dimensional tree. We also provide
fairly general conditions under which the expected formulation in
terms of stopping times does not work.
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