This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Hong, L. J. Search for Related Content

Estimating Quantile Sensitivities

Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
hongl{at}ust.hk

Quantiles of a random performance serve as important alternatives to the usual expected value. They are used in the financial industry as measures of risk and in the service industry as measures of service quality. To manage the quantile of a performance, we need to know how changes in the input parameters affect the output quantiles, which are called quantile sensitivities. In this paper, we show that the quantile sensitivities can be written in the form of conditional expectations. Based on the conditional-expectation form, we first propose an infinitesimal-perturbation-analysis (IPA) estimator. The IPA estimator is asymptotically unbiased, but it is not consistent. We then obtain a consistent estimator by dividing data into batches and averaging the IPA estimates of all batches. The estimator satisfies a central limit theorem for the i.i.d. data, and the rate of convergence is strictly slower than n^–1/3. The numerical results show that the estimator works well for practical problems.

Subject classifications: quantile; value-at-risk; sensitivity analysis; simulation; statistical analysis.
History: Received March 2006; revision received July 2007; accepted September 2007.

This article has been cited by other articles:

				M. C. Fu, L. J. Hong, and J.-Q. Hu Conditional Monte Carlo Estimation of Quantile Sensitivities Management Science, December 1, 2009; 55(12): 2019 - 2027. [Abstract] [PDF]