Scenario reliability assessment for CVaR minimisation in two-stage stochastic programs

Reliable scenarios are needed to obtain a high-quality solution to a stochastic program. Considering sets of scenarios and corresponding observed values of the uncertain parameters over a collection of historical instances, reliability is defined loosely as goodness of the scenarios' fit to the observations. For two-stage, risk-neutral models, a statistical tool was developed previously to assess the reliability of any given scenario generation method. This tool can diagnose over- or under-dispersion and/or bias in the scenario sets. For risk-averse decision makers who aim to minimise conditional value-at-risk (CVaR), only the scenarios that define the upper tail of the optimal cost distribution at the optimal solution are important. We develop a tool to assess the reliability of these so-called effective scenarios for CVaR minimisation. Simulation studies of a financial investment problem demonstrate the ability of the tool to detect mismatches in mean, variance, or kurtosis between scenarios and the corresponding observations.