  Measuring and managing risk has become crucial in modern decision making
under stochastic uncertainty. In two-stage stochastic programming, mean risk
models are essentially defined by a parametric recourse problem and a
quantification of risk. From the perspective of qualitative robustness theory,
we discuss sufficient conditions for continuity of the resulting objective
functions with respect to perturbation of the underlying probability measure.
Our approach covers a fairly comprehensive class of both stochastic-programming
related risk measures and relevant recourse models. Not only this unifies
previous approaches but also extends known stability results for two-stage
stochastic programs to models with mixed-integer quadratic recourse and
mixed-integer convex recourse, respectively.
