 These characterizations allow us to study the effect of the change of numeraire on the corresponding super and subhedging model-free prices. It turns out that, for \mbox{%DIFAUXCMD \cite{BrenierMartingale}\hspace{0pt}%DIFAUXCMD 's construction, the change of numeraire can be viewed as a mirror coupling for positive martingales, while for \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013} }\hspace{0pt}%DIFAUXCMD it }  }\hspace{0pt}%DIFAUXCMD } exchanges forward start straddles of type I and type II giving also that the optimal transport plan in the subhedging problems is the same for both types of options.
<clarity>  These characterizations allow us to study the effect of the change of numeraire on the corresponding super and subhedging model-free prices. It turns out that, for \mbox{%DIFAUXCMD \cite{BrenierMartingale}\hspace{0pt}%DIFAUXCMD 's construction, the change of numeraire can be viewed as a mirror coupling for positive martingales, while for \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013} }\hspace{0pt}%DIFAUXCMD it }  }\hspace{0pt}%DIFAUXCMD } exchanges forward start straddles of type I and type II giving also that the optimal transport plan in the subhedging problems is the same for both types of options.
 These characterizations allow us to study the effect of the change of numeraire }\hspace{0pt}%DIFAUXCMD 's construction, the change of numeraire can be viewed as a mirror coupling for positive martingales, while for \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013} }\hspace{0pt}%DIFAUXCMD it } }\hspace{0pt}%DIFAUXCMD } exchanges forward start straddles of type I and type II giving also that the optimal transport plan in the subhedging problems is the same for both types of options.