Before revision:  It turns out that, for BrenierMartingale's optimal transport plan , the change of numeraire can be viewed as a mirror coupling for positive martingales, while for HobsonKlimmek2013 it 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.
After revision:  It turns out that, for BrenierMartingale's construction , the change of numeraire can be viewed as a mirror coupling for positive martingales, while for HobsonKlimmek2013 it 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.