IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v20y2014i3p167-171n1.html
   My bibliography  Save this article

Quasi-Monte Carlo: A high-dimensional experiment

Author

Listed:
  • Sobol Ilya M.

    (Keldysh Institute of Applied Mathematics, 4, Miusskaya sq., Moscow, 125047, Russia)

  • Shukhman Boris V.

    (18-5 Vereyken Crescent, Petawawa, Ontario, K8H-2C5, Canada)

Abstract

Certain very high-dimensional integrals can be efficiently approximated by quasi-Monte Carlo (q-MC) methods. If the average dimension of the integrand is small, the convergence rate can be near to 1/N, where N is the sample size.

Suggested Citation

  • Sobol Ilya M. & Shukhman Boris V., 2014. "Quasi-Monte Carlo: A high-dimensional experiment," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 167-171, September.
    • Handle: RePEc:bpj:mcmeap:v:20:y:2014:i:3:p:167-171:n:1
    DOI: 10.1515/mcma-2013-0022
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma-2013-0022
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mcma-2013-0022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    2. Ilya M. Sobol’ & Boris V. Shukhman, 1995. "Integration With Quasirandom Sequences: Numerical Experience," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 263-275.
    3. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Marco Bianchetti & Sergei Kucherenko & Stefano Scoleri, 2015. "Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis," Papers 1504.02896, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiaoqun Wang, 2016. "Handling Discontinuities in Financial Engineering: Good Path Simulation and Smoothing," Operations Research, INFORMS, vol. 64(2), pages 297-314, April.
    2. 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.
    3. Marco Bianchetti & Sergei Kucherenko & Stefano Scoleri, 2015. "Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis," Papers 1504.02896, arXiv.org.
    4. Xiaoqun Wang, 2009. "Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 488-504, August.
    5. 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.
    6. Sobol, I.M., 1998. "On quasi-Monte Carlo integrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 103-112.
    7. Sobol’, I.M & Asotsky, D.I, 2003. "One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 255-263.
    8. George Chang, 2018. "Examining the Efficiency of American Put Option Pricing by Monte Carlo Methods with Variance Reduction," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 10(2), pages 10-13, February.
    9. Mercadier Cécile & Ressel Paul, 2021. "Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application," Dependence Modeling, De Gruyter, vol. 9(1), pages 179-198, January.
    10. John Rust & Joseph Traub & Henryk Wozniakowski, 1999. "No Curse of Dimensionality for Contraction Fixed Points Even in the Worst Case," Computational Economics 9902001, University Library of Munich, Germany.
    11. Pierre L’Ecuyer, 2009. "Quasi-Monte Carlo methods with applications in finance," Finance and Stochastics, Springer, vol. 13(3), pages 307-349, September.
    12. Sobol Ilya M. & Shukhman Boris V., 2020. "QMC integration errors and quasi-asymptotics," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 171-176, September.
    13. Aintablian, Sebouh & Khoury, Wissam El, 2017. "A simulation on the presence of competing bidders in mergers and acquisitions," Finance Research Letters, Elsevier, vol. 22(C), pages 233-243.
    14. Kucherenko, S. & Rodriguez-Fernandez, M. & Pantelides, C. & Shah, N., 2009. "Monte Carlo evaluation of derivative-based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1135-1148.
    15. 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.
    16. Eichler Andreas & Leobacher Gunther & Zellinger Heidrun, 2011. "Calibration of financial models using quasi-Monte Carlo," Monte Carlo Methods and Applications, De Gruyter, vol. 17(2), pages 99-131, January.
    17. Xiaoqun Wang, 2006. "On the Effects of Dimension Reduction Techniques on Some High-Dimensional Problems in Finance," Operations Research, INFORMS, vol. 54(6), pages 1063-1078, December.
    18. Krupenev, Dmitry & Boyarkin, Denis & Iakubovskii, Dmitrii, 2020. "Improvement in the computational efficiency of a technique for assessing the reliability of electric power systems based on the Monte Carlo method," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    19. Tan, Ken Seng & Boyle, Phelim P., 2000. "Applications of randomized low discrepancy sequences to the valuation of complex securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1747-1782, October.
    20. Lamboni, Matieyendou, 2021. "Derivative-based integral equalities and inequality: A proxy-measure for sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 137-161.

    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:bpj:mcmeap:v:20:y:2014:i:3:p:167-171:n:1. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.