Efficient global estimation of conditional-value-at-risk through stochastic kriging and extreme value theory

Abstract

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.