  This paper demonstrates a practical method for computing the solution of an
expectation-constrained robust maximization problem with immediate applications
to model-free no-arbitrage bounds and super-replication values for many
financial derivatives. While the previous literature has connected
super-replication values to a convex minimization problem whose objective
function is related to a sequence of iterated concave envelopes, we show how
this whole process can be encoded in a single convex minimization problem. The
natural finite-dimensional approximation of this minimization problem results
in an easily-implementable sparse linear program. We highlight this technique
by obtaining no-arbitrage bounds on the prices of forward-starting options,
continuously-monitored variance swaps, and discretely-monitored gamma swaps,
each subject to observed bid-ask spreads of finitely-many vanilla options.
