Control variates for quantile estimation
Management Science
Likelihood ratio gradient estimation for stochastic systems
Communications of the ACM - Special issue on simulation
Estimating security price derivatives using simulation
Management Science
Control Variates for Probability and Quantile Estimation
Management Science
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Variance Reduction Techniques for Estimating Value-at-Risk
Management Science
Probabilistic Error Bounds for Simulation Quantile Estimators
Management Science
Optimizing cost and performance for multihoming
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
Simulating Sensitivities of Conditional Value at Risk
Management Science
Conditional Monte Carlo Estimation of Quantile Sensitivities
Management Science
Quantile Sensitivity Estimation
NET-COOP '09 Proceedings of the 3rd Euro-NF Conference on Network Control and Optimization
Kernel Estimation of the Greeks for Options with Discontinuous Payoffs
Operations Research
A brief introduction to optimization via simulation
Winter Simulation Conference
Sensitivity analysis for barrier options
Winter Simulation Conference
Confidence intervals for quantiles when applying variance-reduction techniques
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Monte Carlo estimation of value-at-risk, conditional value-at-risk and their sensitivities
Proceedings of the Winter Simulation Conference
Confidence intervals for quantiles and value-at-risk when applying importance sampling
Proceedings of the Winter Simulation Conference
Proceedings of the Winter Simulation Conference
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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.