Continuity Properties of Expectation Functions in Stochastic Integer Programming

Sufficient conditions for the (Lipschitz) continuity of the expectation of second-stage costs are given for two-stage stochastic programs, where the optimization problem in the second stage is a mixed-integer linear program. We also present counterexamples to show that, in general, the results can no longer be maintained when relaxing assumptions as well as multivariate probability distributions for which the theory works.