IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1207.2452.html
   My bibliography  Save this paper

A new approach to unbiased estimation for SDE's

Author

Listed:
  • Chang-han Rhee
  • Peter W. Glynn

Abstract

In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to multi-level Monte Carlo and provides a simple mechanism for constructing a finite variance unbiased estimator with "square root convergence rate" whenever one has available a scheme that produces strong error of order greater than 1/2 for the path functional under consideration.

Suggested Citation

  • Chang-han Rhee & Peter W. Glynn, 2012. "A new approach to unbiased estimation for SDE's," Papers 1207.2452, arXiv.org.
    • Handle: RePEc:arx:papers:1207.2452
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1207.2452
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    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. Li, Yuanbo & Chan, Chu Kin & Yau, Chun Yip & Ng, Wai Leong & Lam, Henry, 2024. "Burn-in selection in simulating stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    2. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.

    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. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    2. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
    3. Jian Wang & Xiang Gao & Zhili Sun, 2021. "A Multilevel Simulation Method for Time-Variant Reliability Analysis," Sustainability, MDPI, vol. 13(7), pages 1-16, March.
    4. Ahmed Kebaier & J'er^ome Lelong, 2015. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Papers 1510.03590, arXiv.org, revised Jul 2017.
    5. Stéphane Crépey & Noufel Frikha & Azar Louzi & Gilles Pagès, 2023. "Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04304985, HAL.
    6. Wei Fang & Zhenru Wang & Michael B. Giles & Chris H. Jackson & Nicky J. Welton & Christophe Andrieu & Howard Thom, 2022. "Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information," Medical Decision Making, , vol. 42(2), pages 168-181, February.
    7. Lay Harold A. & Colgin Zane & Reshniak Viktor & Khaliq Abdul Q. M., 2018. "On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 309-321, December.
    8. Hideyuki Tanaka & Toshihiro Yamada, 2012. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method," Papers 1210.0670, arXiv.org, revised Nov 2013.
    9. Nagy Shady Ahmed & El-Beltagy Mohamed A. & Wafa Mohamed, 2020. "Multilevel Monte Carlo by using the Halton sequence," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 193-203, September.
    10. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Post-Print hal-02430430, HAL.
    11. Lokman A. Abbas-Turki & Stéphane Crépey & Babacar Diallo, 2018. "Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-40, September.
    12. Simonella, Roberta & Vázquez, Carlos, 2023. "XVA in a multi-currency setting with stochastic foreign exchange rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 59-79.
    13. Hoel Håkon & von Schwerin Erik & Szepessy Anders & Tempone Raúl, 2014. "Implementation and analysis of an adaptive multilevel Monte Carlo algorithm," Monte Carlo Methods and Applications, De Gruyter, vol. 20(1), pages 1-41, March.
    14. 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.
    15. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Working Papers hal-02430430, HAL.
    16. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
    17. Jorge Ignacio Gonz'alez C'azares & Aleksandar Mijatovi'c & Ger'onimo Uribe Bravo, 2018. "Geometrically Convergent Simulation of the Extrema of L\'{e}vy Processes," Papers 1810.11039, arXiv.org, revised Jun 2021.
    18. Volk-Makarewicz, Warren & Borovkova, Svetlana & Heidergott, Bernd, 2022. "Assessing the impact of jumps in an option pricing model: A gradient estimation approach," European Journal of Operational Research, Elsevier, vol. 298(2), pages 740-751.
    19. K. Bujok & B. M. Hambly & C. Reisinger, 2015. "Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 579-604, September.
    20. Weinan E & Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse, 2021. "Multilevel Picard iterations for solving smooth semilinear parabolic heat equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-31, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1207.2452. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.