Before revision:  we first specialize the optimal transport plan introduced in \mbox{%DIFAUXCMD BeiglJuil0pt%DIFAUXCMD , following the construction of \mbox{%DIFAUXCMD BrenierMartingale}0pt%DIFAUXCMD , }  as well as the one 0pt%DIFAUXCMD and further studied in \mbox{%DIFAUXCMD BrenierMartingale}\hspace{0pt}%DIFAUXCMD . We show that, } in \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013}\hspace{0pt}%DIFAUXCMD , to } the case of positive martingales and a single maximizer for the difference between the c.d.f.'s of the two marginals. These characterizations allow us to study the effect of the change of numeraire on the corresponding super and subhedging model-free prices.
After revision:  we first specialize the optimal transport plan introduced in \mbox{%DIFAUXCMD BeiglJuil0pt%DIFAUXCMD , following the construction of \mbox{%DIFAUXCMD BrenierMartingale}0pt%DIFAUXCMD , } as well as the one 0pt%DIFAUXCMD and further studied in \mbox{%DIFAUXCMD BrenierMartingale}\hspace{0pt}%DIFAUXCMD . We show that, } in \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013}\hspace{0pt}%DIFAUXCMD , to } the case of positive martingales , a suitable change of numeraire on the corresponding super and subhedging model-free prices.