Minimax identity with robust utility functional for a nonconcave utility
Volume 10, Issue 1 (2023), pp. 19–35
Pub. online: 28 October 2022
Type: Research Article
Open Access
Open Access
Received
11 July 2022
11 July 2022
Revised
25 September 2022
25 September 2022
Accepted
12 October 2022
12 October 2022
Published
28 October 2022
28 October 2022
Abstract
The minimax identity for a nondecreasing upper-semicontinuous utility function satisfying mild growth assumption is studied. In contrast to the classical setting, concavity of the utility function is not asumed. By considering the concave envelope of the utility function, equalities and inequalities between the robust utility functionals of an initial utility function and its concavification are obtained. Furthermore, similar equalities and inequalities are proved in the case of implementing an upper bound on the final endowment of the initial model.
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