Change of numeraire and American options

The change of numéraire technique is a standard tool in mathematical finance. We apply it to the analysis of the value and the hedging strategies of American options. The change of numéraire is particularly powerful if the option is written on more assets and has a positively homogeneous payoff. In this case, the option writer doesn't need the riskless bond to hedge his position. We treat some examples as the Margrabe option on two stocks paying continuous dividends and the best of two assets option. Thanks to variational inequalities we are able to give numerical results for the pricing and the hedging of such a kind of American options.