  This work is devoted to an analysis of exact penalty functions and optimality
conditions for nonsmooth two-stage stochastic programming problems. To this
end, we first study the co-/quasi-differentiability of the expectation of
nonsmooth random integrands and obtain explicit formulae for its co- and
quasidifferential under some natural assumptions on the integrand. Then we
analyse exact penalty functions for a variational reformulation of two-stage
stochastic programming problems and obtain sufficient conditions for the global
exactness of these functions with two different penalty terms. In the end of
the paper, we combine our results on the co-/quasi-differentiability of the
expectation of nonsmooth random integrands and exact penalty functions to
derive optimality conditions for nonsmooth two-stage stochastic programming
problems in terms of codifferentials.
