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Most notably, the upper level goal function in the optimistic setting lacks lower semicontinuity and the existence of an optimal solution cannot be guaranteed under standard assumptions. In this paper, we study a setting where the right-hand side of the lower level constraint system is affected by the leader\u2019s choice as well as the realization of some random vector. Assuming that only the follower decides under complete information, we employ a convex risk measure to assess the upper level outcome. Confining the analysis to the cases where the lower level feasible set is finite, we provide sufficient conditions for H\u00f6lder continuity of the leader\u2019s risk functional and draw conclusions about the existence of optimal solutions. Finally, we examine qualitative stability with respect to perturbations of the underlying probability measure. 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