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Conditional Monte Carlo Estimation of Quantile Sensitivities


  • Michael C. Fu

    () (Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • L. Jeff Hong

    () (Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • Jian-Qiang Hu

    () (Department of Management Science, School of Management, Fudan University, 200433 Shanghai, China)


Estimating quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57 118-130) derived a batched infinitesimal perturbation analysis estimator for quantile sensitivities, and Liu and Hong (Liu, G., L. J. Hong. 2009. Kernel estimation of quantile sensitivities. Naval Res. Logist. 56 511-525) derived a kernel estimator. Both of these estimators are consistent with convergence rates bounded by n -1/3 and n -2/5 , respectively. In this paper, we use conditional Monte Carlo to derive a consistent quantile sensitivity estimator that improves upon these convergence rates and requires no batching or binning. We illustrate the new estimator using a simple but realistic portfolio credit risk example, for which the previous work is inapplicable.

Suggested Citation

  • Michael C. Fu & L. Jeff Hong & Jian-Qiang Hu, 2009. "Conditional Monte Carlo Estimation of Quantile Sensitivities," Management Science, INFORMS, vol. 55(12), pages 2019-2027, December.
  • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:12:p:2019-2027

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    Cited by:

    1. J P C Kleijnen & W C M van Beers, 2013. "Monotonicity-preserving bootstrapped Kriging metamodels for expensive simulations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(5), pages 708-717, May.
    2. Chang, Kuo-Hao, 2015. "A direct search method for unconstrained quantile-based simulation optimization," European Journal of Operational Research, Elsevier, vol. 246(2), pages 487-495.
    3. Bernd Heidergott & Warren Volk-Makarewicz, 2013. "A Measure-Valued Differentiation Approach to Sensitivity Analysis of Quantiles," Tinbergen Institute Discussion Papers 13-082/III, Tinbergen Institute.
    4. Begen, Mehmet A. & Pun, Hubert & Yan, Xinghao, 2016. "Supply and demand uncertainty reduction efforts and cost comparison," International Journal of Production Economics, Elsevier, vol. 180(C), pages 125-134.
    5. Kleijnen, Jack P.C. & Pierreval, Henri & Zhang, Jin, 2011. "Methodology for determining the acceptability of system designs in uncertain environments," European Journal of Operational Research, Elsevier, vol. 209(2), pages 176-183, March.
    6. Kellner, Ralf & Rösch, Daniel, 2016. "Quantifying market risk with Value-at-Risk or Expected Shortfall? – Consequences for capital requirements and model risk," Journal of Economic Dynamics and Control, Elsevier, vol. 68(C), pages 45-63.


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