  We regard the optimal reinsurance problem as an iterated optimal transport
problem between a (known) initial and an (unknown) resulting risk exposure of
the insurer. We also provide conditions that allow to characterize the support
of optimal treaties, and show how this can be used to deduce the shape of the
optimal contract, reducing the task to a finite-dimensional optimization
problem, for which standard techniques can be applied. The proposed approach
provides a general framework that encompasses many reinsurance problems, which
we illustrate in several concrete examples, providing alternative proofs of
classical optimal reinsurance results as well as establishing new optimality
results, some of which contain optimal treaties that involve external
randomness.
