On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs

Details On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs

2005-02-09

arxiv.org/abs/math/0502189v1

Mathematics

Probability

Scientific paper

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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