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Some Guidelines and Guarantees for Common Random Numbers

Author

Listed:
  • Paul Glasserman

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • David D. Yao

    (IE/OR Department, Columbia University, New York, New York 10027)

Abstract

Common random numbers (CRN) is a widely-used technique for reducing variance in comparing stochastic systems through simulation. Its popularity derives from its intuitive appeal and ease of implementation. However, though CRN has been observed to work well with a broad range of models, the class of systems for which it is provably advantageous has remained rather limited. This paper has two purposes: We first discuss the effectiveness and optimality of CRN in a general setting, stressing the roles played by monotonicity and continuity properties. We then present specific, new classes of systems and comparisons for which CRN is beneficial and even optimal. Our conclusions for these systems are largely consistent with simulation practice and lend further theoretical support to folklore. Our results differ from those of previous analyses primarily because we put conditions on the timing of events, rather than the sequence of states, in a discrete-event simulation. We formulate our results in three settings corresponding to three applications of CRN: distributional comparisons, structural comparisons, and sensitivity analysis. In each case, we make use of conditions that simultaneously ensure monotonicity and continuity in the timing of events. These properties are established through explicit recursions for event epochs in terms of increasing, continuous functions.

Suggested Citation

  • Paul Glasserman & David D. Yao, 1992. "Some Guidelines and Guarantees for Common Random Numbers," Management Science, INFORMS, vol. 38(6), pages 884-908, June.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:6:p:884-908
    DOI: 10.1287/mnsc.38.6.884
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    Citations

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    Cited by:

    1. Eric Benhamou, 2000. "A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks," FMG Discussion Papers dp350, Financial Markets Group.
    2. Jiajie Kong & Robert Lund, 2023. "Seasonal count time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 93-124, January.
    3. Sheldon H. Jacobson & Enver Yücesan, 1999. "On the Complexity of Verifying Structural Properties of Discrete Event Simulation Models," Operations Research, INFORMS, vol. 47(3), pages 476-481, June.
    4. Guillaume Bernis & Emmanuel Gobet & Arturo Kohatsu‐Higa, 2003. "Monte Carlo Evaluation of Greeks for Multidimensional Barrier and Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 99-113, January.
    5. Nathan L. Kleinman & James C. Spall & Daniel Q. Naiman, 1999. "Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers," Management Science, INFORMS, vol. 45(11), pages 1570-1578, November.
    6. Michael C. Fu & Jian-Qiang Hu & Chun-Hung Chen & Xiaoping Xiong, 2007. "Simulation Allocation for Determining the Best Design in the Presence of Correlated Sampling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 101-111, February.
    7. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    8. Shuowen Chen, 2022. "Indirect Inference for Nonlinear Panel Models with Fixed Effects," Papers 2203.10683, arXiv.org, revised Apr 2022.
    9. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    10. Chih, Mingchang, 2023. "Stochastic stability analysis of particle swarm optimization with pseudo random number assignment strategy," European Journal of Operational Research, Elsevier, vol. 305(2), pages 562-593.
    11. Andrea Maria Zanchettin, 2022. "Robust scheduling and dispatching rules for high-mix collaborative manufacturing systems," Flexible Services and Manufacturing Journal, Springer, vol. 34(2), pages 293-316, June.
    12. Saif, Ahmed & Elhedhli, Samir, 2016. "Cold supply chain design with environmental considerations: A simulation-optimization approach," European Journal of Operational Research, Elsevier, vol. 251(1), pages 274-287.
    13. Benhamou, Eric, 2000. "A generalisation of Malliavin weighted scheme for fast computation of the Greeks," LSE Research Online Documents on Economics 119105, London School of Economics and Political Science, LSE Library.
    14. Chaudhuri, Anirban & Kramer, Boris & Willcox, Karen E., 2020. "Information Reuse for Importance Sampling in Reliability-Based Design Optimization," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    15. Dag Kolsrud, 2008. "Stochastic Ceteris Paribus Simulations," Computational Economics, Springer;Society for Computational Economics, vol. 31(1), pages 21-43, February.
    16. Marvin K. Nakayama & Perwez Shahabuddin, 1998. "Likelihood Ratio Derivative Estimation for Finite-Time Performance Measures in Generalized Semi-Markov Processes," Management Science, INFORMS, vol. 44(10), pages 1426-1441, October.
    17. B. Heidergott & F. J. Vázquez-Abad, 2008. "Measure-Valued Differentiation for Markov Chains," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 187-209, February.
    18. Davis, Mark H.A. & Johansson, Martin P., 2006. "Malliavin Monte Carlo Greeks for jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 101-129, January.

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