J. Blanchet, F. He and H. Lam, “Computing worst-case expectations given marginals via simulation,” 2017 Winter Simulation Conference (WSC), Las Vegas, NV, USA, 2017, pp. 2315-2323, doi: 10.1109/WSC.2017.8247962. keywords: {Convergence;Monte Carlo methods;Optimization;Estimation;Random variables;Standards;Algorithm design and analysis},

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Abstract

We study a direct Monte-Carlo-based approach for computing the worst-case expectation of two multidimensional random variables given a specification of their marginal distributions. This problem is motivated by several applications in risk quantification and statistics. We show that if one of the random variables takes finitely many values, a direct Monte Carlo approach allows to evaluate such worst case expectation with O(n -1/2 ) convergence rate as the number of Monte Carlo samples, n, increases to infinity.

Authors
Jose Blanchet, Fei He, Henry Lam
Publication date
2017/12/3
Conference
2017 Winter Simulation Conference (WSC)
Pages
2315-2323
Publisher
IEEE