  We study the minimax identity for a non-decreasing upper-semicontinuous
utility function satisfying mild growth assumption. In contrast to the
classical setting, we do not impose the assumption that the utility function is
concave. By considering the concave envelope of the utility function we obtain
equalities and inequalities between the robust utility functionals of an
initial utility function and its concavification. Furthermore, we prove similar
equalities and inequalities in the case of implementing an upper bound on the
final endowment of the initial model.
