Quantitative continuity of optimal solution sets to convex stochastic programs with (linear) complete recourse and random right-hand sides is investigated when the underlying probability measure varies in a metric space. The central result asserts that, under a strong-convexity condition for the expected recourse in the unperturbed problem, optimal tenders behave Hölder-continuous with respect to a Wasserstein metric. For linear stochastic programs this carries over to the Hausdorff distance of optimal solution sets A general sufficient condition for the crucial strong-convexity assumption is given and verified for recourse problems with separable and nonseparable objectives.
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Römisch et al. (1993) studied this question.
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