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We study the minimax identity for a non-decreasing upper-semicontinuousutility function satisfying mild growth assumption. In contrast to theclassical setting, we do not impose the assumption that the utility function isconcave. By considering the concave envelope of the utility function we obtainequalities and inequalities between the robust utility functionals of aninitial utility function and its concavification. Furthermore, we prove similarequalities and inequalities in the case of implementing an upper bound on thefinal endowment of the initial model.

Minimax identity with robust utility functional for a non-concave utility