  By investigating model-independent bounds for exotic options in financial
mathematics, a martingale version of the Monge-Kantorovich mass transport
problem was introduced in \cite{BeiglbockHenry
LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the
one-dimensional Brenier's theorem to the present martingale version. We provide
the explicit martingale optimal transference plans for a remarkable class of
coupling functions corresponding to the lower and upper bounds. These explicit
extremal probability measures coincide with the unique left and right monotone
martingale transference plans, which were introduced in \cite{BeiglbockJuillet}
by suitable adaptation of the notion of cyclic monotonicity. Instead, our
approach relies heavily on the (weak) duality result stated in
\cite{BeiglbockHenry-LaborderePenkner}, and provides, as a by-product, an
explicit expression for the corresponding optimal semi-static hedging
strategies. We finally provide an extension to the multiple marginals case.
