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

  • Armin Khayyer [1] ; Joseph J. Kennedy [1] ; Alexander Vinel [1]
    1. [1] Auburn University

      Auburn University

      Estados Unidos

  • Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 34, Nº. 1, 2026, págs. 40-75
  • Idioma: inglés
  • DOI: 10.1007/s11750-025-00702-5
  • Enlaces
  • Resumen

    • We consider the problem of evaluating risk for a stochastic system (for example, a complex stochastic simulation) with many possible input parameter values. Two sources of computational burden can be identified: the effort associated with sampling (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 using Extreme Value Theory (EVT) estimations (we employ Peak-over-Threshold method), 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 metamodeling framework, stochastic kriging, that is based on EVT-based estimation for a class of coherent law-invariant comonotone additive measures of risk, primarily focusing on Conditional Value-at-Risk (CVaR). The proposed approach requires an efficient estimator of the intrinsic variance, and so, we demonstrate how EVT can be used to derive it. This then allows us to combine a number of results in metamodeling and estimation literatures to present a purely EVT-based stochastic kriging model for predicting CVaR. We also perform a case study, outlining promising use cases, and conditions when the EVT-based approach outperforms simpler empirical estimators. While the improvement is modest relative to the best existing approach based on empirical estimation, it is statistically significant, particularly for cases where the computational budget is sufficient to obtain reliable EVT estimates.

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