Browsing by Author "Hu, Jian-Qiang"

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    Application of Perturbation Analysis to the Design and Analysis of Control Charts
    (1997) Fu, Michael C.; Hu, Jian-Qiang; ISR
    The design of control charts in statistical quality control addresses the optimal selection of the design parameters such as the sampling frequency and the control limits; and includes sensitivity analysis with respect to system parameters such as the various process parameters and the economic costs of sampling. The advent of more complicated control chart schemes has necessitated the use of Monte Carlo simulation in the design process, particularly in the evaluation of performance measures such as average run length. In this paper, we apply perturbation analysis to derive gradient estimators that can be used in gradient-based optimization algorithms and in sensitivity analysis when Monte Carlo simulation is employed. We illustrate the technique on a simple Shewhart control chart and on a more complicated control chart that includes the exponentially- weighted moving average control chart as a special case.
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    Gradient Estimation for Queues with Non-identical Servers
    (1993) Fu, Michael C.; Hu, Jian-Qiang; Nagi, Rakesh; ISR
    We consider a single-queue system with multiple servers that are non-identical. Our interest is in applying the technique of perturbation analysis to estimate derivatives of mean steady- state system time. Because infinitesimal perturbation analysis yields biased estimates for this problem, we apply smoothed perturbation analysis to get unbiased estimators. In the most general cases, the estimators require additional simulation, so we propose an approximation to eliminate this. For two servers, we give an analytical proof of unbiasedness in steady state for the Markovian case. We provide simulation results for both Markovian and non-Markovian examples, and compare the performance with regenerative likelihood ratio estimators.
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    Online Appendix for “Gradient-Based Myopic Allocation Policy: An Efficient Sampling Procedure in a Low-Confidence Scenario”
    (2017) Peng, Yijie; Chen, Chun-Hung; Fu, Michael; Hu, Jian-Qiang
    This is the online appendix, which includes theoretical and numerical supplements containing some technical details and three additional numerical examples, which could not fit in the main body due to page limits by the journal for a technical note. The abstract for the main body is as follows: In this note, we study a simulation optimization problem of selecting the alternative with the best performance from a finite set, or a so-called ranking and selection problem, in a special low-confidence scenario. The most popular sampling allocation procedures in ranking and selection do not perform well in this scenario, because they all ignore certain induced correlations that significantly affect the probability of correct selection in this scenario. We propose a gradient-based myopic allocation policy (G-MAP) that takes the induced correlations into account, reflecting a trade-off between the induced correlation and the two factors (mean-variance) found in the optimal computing budget allocation formula. Numerical experiments substantiate the efficiency of the new procedure in the low-confidence scenario.
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    Online Supplement to `Efficient Simulation Resource Sharing and Allocation for Selecting the Best'
    (2012) Peng, Yijie; Chen, Chun-Hung; Fu, Michael; Hu, Jian-Qiang
    This is the online supplement to the article by the same authors, "Efficient Simulation Resource Sharing and Allocation for Selecting the Best," published in the IEEE Transactions on Automatic Control.
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    Sensitivity Analysis for Monte Carlo Simulation of Option Pricing
    (1995) Fu, Michael C.; Hu, Jian-Qiang
    Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but also estimates of the sensitivities of the option value to various parameters of the model. Both European and American options are considered, starting with simple analytically tractable models to present the idea and proceeding to more complicated examples. We then propose an approach for the pricing of options with early exercise features by incorporating the gradient estimates in an iterative stochastic approximation algorithm. The procedure is illustrated in a simple example estimating the option value of an American call. Numerical results indicate that the additional computational effort required over that required to estimate a European option is relatively small.