Scenario generation for stochastic programs with tail risk measure

Tail risk measures such as Value-at-Risk and Conditional Value-at-Risk are used in stochastic programming to mitigate or reduce the probability of large losses. However, because tail risk measures only depend on the upper tail of a distribution, scenario generation for these problems is difficult as standard methods such as sampling will typically inadequately represent these areas. We present a problem-based approach to scenario generation for stochastic programs which use tail risk measures, and demonstrate this approach on a class of portfolio selection problems.