IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v332y2018icp48-57.html
   My bibliography  Save this article

Generalized two-step Maruyama methods for stochastic differential equations

Author

Listed:
  • Ren, Quanwei
  • Tian, Hongjiong

Abstract

In this paper, we propose generalized two-step Maruyama methods for solving Itô stochastic differential equations. Numerical analysis concerning consistency, convergence and numerical stability in the mean-square sense is presented. We derive sufficient and necessary conditions for linear mean-square stability of the generalized two-step Maruyama methods. We compare the stability region of the generalized two-step Maruyama methods of Adams type with that of the corresponding two-step Maruyama methods of Adams type and show that our proposed methods have better linear mean-square stability. A numerical example is given to confirm our theoretical results.

Suggested Citation

  • Ren, Quanwei & Tian, Hongjiong, 2018. "Generalized two-step Maruyama methods for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 48-57.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:48-57
    DOI: 10.1016/j.amc.2018.03.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318301681
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.03.003?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. P. E. Kloeden & Eckhard Platen, 1992. "Higher-order implicit strong numerical schemes for stochastic differential equations," Published Paper Series 1992-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    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. D’Ambrosio, Raffaele & Scalone, Carmela, 2021. "Two-step Runge-Kutta methods for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 403(C).

    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. Hofmann, Norbert, 1995. "Stability of weak numerical schemes for stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 63-68.
    2. Mu Niu & Pokman Cheung & Lizhen Lin & Zhenwen Dai & Neil Lawrence & David Dunson, 2019. "Intrinsic Gaussian processes on complex constrained domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 603-627, July.
    3. Shunwei Zhu & Bo Wang, 2019. "Unified Approach for the Affine and Non-affine Models: An Empirical Analysis on the S&P 500 Volatility Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1421-1442, April.
    4. Eckhard Platen & Renata Rendek, 2009. "Quasi-exact Approximation of Hidden Markov Chain Filters," Research Paper Series 258, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Yin, Zhengwei & Gan, Siqing, 2015. "An error corrected Euler–Maruyama method for stiff stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 630-641.
    6. 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.
    7. Patrick Assonken & Gangaram Ladde, 2017. "Simulation and Calibration of Options Prices under a Levy-Type Stochastic Dynamic and Semi Markov Market Switching Regimes Processes," Applied Economics and Finance, Redfame publishing, vol. 4(1), pages 93-126, January.
    8. Mahmoud A. Eissa & Boping Tian, 2017. "Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects," Energies, MDPI, vol. 10(1), pages 1-19, January.
    9. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    10. Nicola Bruti-Liberati & Eckhard Platen, 2008. "Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations," Research Paper Series 222, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Alejandra López-Pérez & Manuel Febrero-Bande & Wencesalo González-Manteiga, 2021. "Parametric Estimation of Diffusion Processes: A Review and Comparative Study," Mathematics, MDPI, vol. 9(8), pages 1-27, April.
    12. Eckhard Platen & Renata Rendek, 2009. "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes," Research Paper Series 259, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Eckhard Platen & Lei Shi, 2008. "On the Numerical Stability of Simulation Methods for SDES," Research Paper Series 234, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013, January-A.
    15. Quansah, Emmanuel & Parshad, Rana D. & Mondal, Sumona, 2017. "Cold induced mortality of the Burmese Python: An explanation via stochastic analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 356-364.
    16. Chassagneux, Jean-François & Richou, Adrien, 2019. "Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4597-4637.
    17. Rupak Chatterjee & Zhenyu Cui & Jiacheng Fan & Mingzhe Liu, 2018. "An efficient and stable method for short maturity Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1470-1486, December.

    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:apmaco:v:332:y:2018:i:c:p:48-57. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.