IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v47y1998i2p287-298.html
   My bibliography  Save this article

Stochastic methods for multiple integrals over unbounded regions

Author

Listed:
  • Genz, Alan

Abstract

Recent work in the development of stochastic methods for multiple integrals over unbounded regions is reviewed and generalized. This includes randomization or deterministic rules, and new stochastic rules for integrals with multivariate Normal weight. Stochastic spherical–radial rules are also discussed. These rules use a spherical–radial transformation of the infinite integration region and combine stochastic rules for the infinite radial interval with stochastic rules for the spherical surface. Example problems taken from Bayesian statistical analysis and computational finance are used to illustrate the use of the different methods.

Suggested Citation

  • Genz, Alan, 1998. "Stochastic methods for multiple integrals over unbounded regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 287-298.
    • Handle: RePEc:eee:matcom:v:47:y:1998:i:2:p:287-298
    DOI: 10.1016/S0378-4754(98)00105-0
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475498001050
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/S0378-4754(98)00105-0?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. Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
    Full references (including those not matched with items on IDEAS)

    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. David Heath & Eckhard Platen, 2002. "A variance reduction technique based on integral representations," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 362-369.
    2. 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.
    3. Jacob Lundgren & Yuri Shpolyanskiy, 2017. "Approaches to Asian Option Pricing with Discrete Dividends," Papers 1702.00994, arXiv.org, revised Mar 2021.
    4. Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
    5. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    6. 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.
    7. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    8. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    9. 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.
    10. Moshe Arye Milevsky & Steven E. Posner, 1999. "Asian Options, The Sum Of Lognormals, And The Reciprocal Gamma Distribution," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 7, pages 203-218, World Scientific Publishing Co. Pte. Ltd..
    11. Armstrong, Michael J., 2001. "The reset decision for segregated fund maturity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 257-269, October.
    12. Siegl, Thomas & F. Tichy, Robert, 2000. "Ruin theory with risk proportional to the free reserve and securitization," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 59-73, February.
    13. John Board & Charles Sutcliffe & William T. Ziemba, 2003. "Applying Operations Research Techniques to Financial Markets," Interfaces, INFORMS, vol. 33(2), pages 12-24, April.
    14. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    15. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    16. Zbigniew Palmowski & Tomasz Serafin, 2020. "Note on simulation pricing of $\pi$-options," Papers 2007.02076, arXiv.org, revised Aug 2020.
    17. Harase Shin, 2019. "Comparison of Sobol’ sequences in financial applications," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 61-74, March.
    18. Boyle, Phelim & Imai, Junichi & Tan, Ken Seng, 2008. "Computation of optimal portfolios using simulation-based dimension reduction," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 327-338, December.
    19. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    20. Aprahamian, Hrayer & Maddah, Bacel, 2015. "Pricing Asian options via compound gamma and orthogonal polynomials," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 21-43.

    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:eee:matcom:v:47:y:1998:i:2:p:287-298. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.