We study robust stochastic optimization problems in the quasi-sure setting indiscrete-time. The strategies are restricted to those taking values in adiscrete set. The optimization problems under consideration are not concave. Weprovide conditions under which a maximizer exists. The class of problemscovered by our robust optimization problem includes optimal stopping andsemi-static trading under Knightian uncertainty. Moreover, it also can beconsidered as an approximation of general nonconcave robust stochasticoptimization problems.
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