IDEAS home Printed from https://ideas.repec.org/h/spr/isochp/978-0-306-48102-4_20.html
   My bibliography  Save this book chapter

Recent Advances in Randomized Quasi-Monte Carlo Methods

In: Modeling Uncertainty

Author

Listed:
  • Pierre L’Ecuyer

    (Université de Montréal)

  • Christiane Lemieux

    (University of Calgary)

Abstract

We survey some of the recent developments on quasi-Monte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a high-dimensional integral. We review several QMC constructions and different randomizations that have been proposed to provide unbiased estimators and for error estimation. Randomizing QMC methods allows us to view them as variance reduction techniques. New and old results on this topic are used to explain how these methods can improve over the MC method in practice. We also discuss how this methodology can be coupled with clever transformations of the integrand in order to reduce the variance further. Additional topics included in this survey are the description of figures of merit used to measure the quality of the constructions underlying these methods, and other related techniques for multidimensional integration.

Suggested Citation

  • Pierre L’Ecuyer & Christiane Lemieux, 2002. "Recent Advances in Randomized Quasi-Monte Carlo Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 419-474, Springer.
    • Handle: RePEc:spr:isochp:978-0-306-48102-4_20
    DOI: 10.1007/0-306-48102-2_20
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vladimir K. Kaishev & Dimitrina S. Dimitrova, 2009. "Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options," Management Science, INFORMS, vol. 55(3), pages 483-496, March.
    2. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, December.
    3. Vandewoestyne, Bart & Chi, Hongmei & Cools, Ronald, 2010. "Computational investigations of scrambled Faure sequences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 522-535.
    4. F. Y. Kuo & W. T. M. Dunsmuir & I. H. Sloan & M. P. Wand & R. S. Womersley, 2008. "Quasi-Monte Carlo for Highly Structured Generalised Response Models," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 239-275, June.
    5. Bastin, Fabian & Cirillo, Cinzia & Toint, Philippe L., 2006. "Application of an adaptive Monte Carlo algorithm to mixed logit estimation," Transportation Research Part B: Methodological, Elsevier, vol. 40(7), pages 577-593, August.
    6. Athanassios N. Avramidis & Pierre L'Ecuyer, 2006. "Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance Gamma Model," Management Science, INFORMS, vol. 52(12), pages 1930-1944, December.
    7. H. Heitsch & H. Leövey & W. Römisch, 2016. "Are Quasi-Monte Carlo algorithms efficient for two-stage stochastic programs?," Computational Optimization and Applications, Springer, vol. 65(3), pages 567-603, December.
    8. Okten, Giray & Eastman, Warren, 2004. "Randomized quasi-Monte Carlo methods in pricing securities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2399-2426, December.
    9. Pierre L’Ecuyer, 2009. "Quasi-Monte Carlo methods with applications in finance," Finance and Stochastics, Springer, vol. 13(3), pages 307-349, September.
    10. Xiaoqun Wang & Ken Seng Tan, 2013. "Pricing and Hedging with Discontinuous Functions: Quasi-Monte Carlo Methods and Dimension Reduction," Management Science, INFORMS, vol. 59(2), pages 376-389, July.
    11. Jank, Wolfgang, 2005. "Quasi-Monte Carlo sampling to improve the efficiency of Monte Carlo EM," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 685-701, April.
    12. L’Ecuyer, P. & Sanvido, C., 2010. "Coupling from the past with randomized quasi-Monte Carlo," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 476-489.
    13. Xing Jin & Michael C. Fu & Xiaoping Xiong, 2003. "Probabilistic Error Bounds for Simulation Quantile Estimators," Management Science, INFORMS, vol. 49(2), pages 230-246, February.
    14. Xiaoqun Wang & Ian H. Sloan, 2011. "Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction," Operations Research, INFORMS, vol. 59(1), pages 80-95, February.
    15. Pierre L’Ecuyer & Florian Puchhammer & Amal Ben Abdellah, 2022. "Monte Carlo and Quasi–Monte Carlo Density Estimation via Conditioning," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1729-1748, May.
    16. Yang Huang & Yongdao Zhou, 2022. "Convergence of Uniformity Criteria and the Application in Numerical Integration," Mathematics, MDPI, vol. 10(19), pages 1-20, October.
    17. Lucio Barabesi, 2003. "A Monte Carlo integration approach to Horvitz-Thompson estimation in replicated environmental designs," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 355-374.
    18. Yumiao Tian & Maorong Ge & Frank Neitzel, 2020. "Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation," Mathematics, MDPI, vol. 8(4), pages 1-15, April.
    19. Zhijian He & Xiaoqun Wang, 2021. "An Integrated Quasi-Monte Carlo Method for Handling High Dimensional Problems with Discontinuities in Financial Engineering," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 693-718, February.
    20. Pierre L'Ecuyer & Christian Lécot & Bruno Tuffin, 2008. "A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains," Operations Research, INFORMS, vol. 56(4), pages 958-975, August.
    21. Baldeaux Jan, 2008. "Quasi-Monte Carlo methods for the Kou model," Monte Carlo Methods and Applications, De Gruyter, vol. 14(4), pages 281-302, January.
    22. Hatem Ben-Ameur & Pierre L'Ecuyer & Christiane Lemieux, 2004. "Combination of General Antithetic Transformations and Control Variables," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 946-960, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:isochp:978-0-306-48102-4_20. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.