Proceedings of the 2020 Winter Simulation Conference
K.-H. Bae, B. Feng, S. Kim, S. Lazarova-Molnar, Z. Zheng, T. Roeder, and R. Thiesing, eds.
EFFICIENT RISK ESTIMATION USING EXTREME
VALUE THEORY AND SIMULATION METAMODELING
Joseph J. Kennedy
Armin Khayyer
Alexander Vinel
Alice E. Smith
Industrial and Systems Engineering
Auburn University
Shelby Center
Auburn, Al 36849, USA
ABSTRACT
This paper considers a new approach for constructing metamodels for capturing tail behavior in stochastic
systems, e.g., simulation outputs. Specifically, we are concerned with the problem of global estimation
of the conditional value-at-risk (CVaR) surface, given (stochastic) responses from a collection of design
points. The approach combines stochastic kriging, which has previously been shown to work well for
metamodeling of discrete-event simulation output, with extreme value theory, which is a powerful statistical
tool for estimating tail behavior. We present the general methodology and promising results of preliminary
computational experiments.
1 INTRODUCTION
Executing and analyzing high-fidelity simulation models covering a wide range of parameters are often
quite computationally expensive, leading to significant attention paid in the literature to the area of
metamodeling, or surrogate modeling, for simulation. Applications that are concerned with characterizing
risk are particularly in need of such efforts. In these applications, the decision-makers are interested in
accurately describing tail behavior for the underlying distributions, which usually requires proportionally
more computational effort to observe sufficient rare events.
This paper proposes a metamodeling approach for globally characterizing a particular tail measure,
Conditional Value-at-Risk (CVaR), combining two relevant methodologies: stochastic kriging (SK) and
the peaks-over-threshold (POT) method for tail estimation. Stochastic kriging has been shown to be a
powerful modeling tool for predicting discrete-event simulation outputs, including forecasting tail measures
(Chen et al. 2012). While Chen et al. (2012) demonstrated promising results, their methodology is
based on empirical (nonparametric) estimators of risk measures. An alternative approach to characterizing
tail behavior has been studied under the umbrella of extreme value theory (EVT). Widely used in many
computational areas, it so far has received rather limited attention in the operations research community
in general and simulation applications in particular. EVT is known to improve tail estimates for various
stochastic systems (McNeil and Saladin 1997). Consequently, in this paper, we are interested in evaluating
whether this improvement persists if used within a metamodeling framework, such as stochastic kriging.
To this end, we propose a two-stage metamodeling framework, which employs the peaks-over-threshold
(POT) method from EVT to estimate CVaR for a set of given design points on the response surface and
then applies stochastic kriging to the estimated values to enable global predictions.
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