It is well known that several solutions to the Skorokhod problem
optimize certain ``cost''- or ``payoff''-functionals. We use the
theory of Monge-Kantorovich transport to study the corresponding
optimization problem. We formulate a dual problem and establish
duality based on the duality theory of optimal transport. Notably
the primal as well as the dual problem have a natural interpretation
in terms of model-independent no arbitrage theory.
In optimal transport the notion of c-monotonicity is used to
characterize the geometry of optimal transport plans. We derive a
similar optimality principle that provides a geometric
characterization of optimal stopping times. We then use this
principle to derive several known solutions to the Skorokhod
embedding problem and also new ones.
This is joint work with Mathias Beiglböck and Alex Cox.