Preference Robust Modified Optimized Certainty Equivalent

Ben-Tal and Teboulle [Management Sci., 32 (1986), pp. 1445--1466] introduce the concept of optimized certainty equivalent (OCE) an uncertain outcome as maximum present value a combination cash to be taken out from income at expected utility remaining income. In this paper, we consider two variations OCE. First, modified OCE by maximizing so that combined quantity is in unified value. Second, situation where true function unknown but it possible use partially available information construct set plausible functions. To mitigate risk arising ambiguity, robust model based on worst-case ambiguity set. case when functions constructed Kantorovich ball centered nominal function, show how corresponding can identified solving linear programs alternatively. We also statistically data-driven environment underlying data are potentially contaminated. Some preliminary numerical results reported demonstrate performance model.