Hedging of American options under transaction costs

Abstract

We consider a continuous-time model of a financial market with proportional transaction costs. Our result is a dual description of the set of initial endowments of self-financing portfolios super-replicating an American-type contingent claim. The latter is a right-continuous adapted vector process describing the number of assets to be delivered at the exercise date. We introduce a specific class of price systems, called coherent, and show that the hedging endowments are those whose “values” are larger than the expected weighted “values” of the payoff process for every coherent price system used for the “evaluation” of the assets.