Continuity and Stability in Two-Stage Stochastic Integer Programming

For two-stage stochastic programs where the optimization problem in the second stage is a mixed-integer linear program continuity of the expectation of second-stage costs jointly in the first-stage strategy and the integrating probability measure is derived. Then, regarding the two-stage stochastic program as a parametric program with the underlying probability measure as parameter, continuity of the locally optimal value and upper semicontinuity of the corresponding set of local solutions are established.