Hedging of American Options under Transaction Costs

International audienceWe consider a continuous-time model of financial market with proportional transaction costs. Our result is a dual description of the set of initial endowments of self-financing portfolios super replicating 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 pay-off process for every coherent price system used for the 'evaluation' of the assets