Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints (Q1885278)

The authors improve earlier results and provide conditions implying Hölder continuity properties of the solution sets of a stochastic program with a probabilistic constraint and \(r\)-concave original probability distribution. Upper Lipschitz continuity property for solution sets under more restrictive conditions on the original program and on perturbed probability measures are also derived. The stability results are illustrated by numerical tests showing the different asymptotic behavior of parametric and nonparametric estimates in a program with a normal probabilistic constraint.