  In this paper a class of combinatorial optimization problems is discussed. It
is assumed that a solution can be constructed in two stages. The current
first-stage costs are precisely known, while the future second-stage costs are
only known to belong to an uncertainty set, which contains a finite number of
scenarios with known probability distribution. A partial solution, chosen in
the first stage, can be completed by performing an optimal recourse action,
after the true second-stage scenario is revealed. A solution minimizing the
Conditional Value at Risk (CVaR) measure is computed. Since expectation and
maximum are boundary cases of CVaR, the model generalizes the traditional
stochastic and robust two-stage approaches, previously discussed in the
existing literature. In this paper some new negative and positive results are
provided for basic combinatorial optimization problems such as the selection or
network problems.
