  Dybvig (1988a,b) solves in a complete market setting the problem of finding a
payoff that is cheapest possible in reaching a given target distribution
("cost-efficient payoff"). In the presence of ambiguity, the distribution of a
payoff is, however, no longer known with certainty. We study the problem of
finding the cheapest possible payoff whose worst-case distribution
stochastically dominates a given target distribution ("robust cost-efficient
payoff") and determine solutions under certain conditions. We study the link
between "robust cost-efficiency" and the maxmin expected utility setting of
Gilboa and Schmeidler, as well as more generally with robust preferences in a
possibly non-expected utility setting. Specifically, we show that solutions to
maxmin robust expected utility are necessarily robust cost-efficient. We
illustrate our study with examples involving uncertainty both on the drift and
on the volatility of the risky asset.
