We investigate the problem of maximizing the robust utility functional inf QEQ EQu(X).
We give the dual characterization for its solution for both a complete and an incomplete
market model. To this end, we introduce the new notion of reverse f-projections and
use techniques developed for f-divergences. This is a suitable tool to reduce the robust
problem to the classical problem of utility maximization under a certain measure: the
reverse f-projection. Furthermore, we give the dual characterization for a closely related
problem, the minimization of expenditures given a minimum level of expected utility in
a robust setting and for an incomplete market.