  We consider the problem of evaluating risk for a system that is modeled by a
complex stochastic simulation with many possible input parameter values. Two
sources of computational burden can be identified: the effort associated with
extensive simulation runs required to accurately represent the tail of the loss
distribution for each set of parameter values, and the computational cost of
evaluating multiple candidate parameter values. The former concern can be
addressed by using Extreme Value Theory (EVT) estimations, which specifically
concentrate on the tails. Meta-modeling approaches are often used to tackle the
latter concern. In this paper, we propose a framework for constructing a
particular meta-modeling framework, stochastic kriging, that is based on
EVT-based estimation for a class of coherent measures of risk. The proposed
approach requires an efficient estimator of the intrinsic variance, and so we
derive an EVT-based expression for it. It then allows us to avoid multiple
replications of the risk measure in each design point, which was required in
similar previously proposed approaches, resulting in a substantial reduction in
computational effort. We then perform a case study, outlining promising use
cases, and conditions when the EVT-based approach outperforms simpler empirical
estimators.
