IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i6p588-d514106.html
   My bibliography  Save this article

A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models

Author

Listed:
  • Yang Li

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Taitao Feng

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Yaolei Wang

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Yifei Xin

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

Abstract

In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results.

Suggested Citation

  • Yang Li & Taitao Feng & Yaolei Wang & Yifei Xin, 2021. "A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models," Mathematics, MDPI, vol. 9(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:588-:d:514106
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/6/588/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/6/588/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yuan, Chenggui & Mao, Xuerong, 2004. "Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 223-235.
    2. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2007.
    3. Zhao, Jingjun & Yi, Yulian & Xu, Yang, 2021. "Strong convergence of explicit schemes for highly nonlinear stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    4. He, Hangfeng & Qi, Wenhai & Kao, Yonggui, 2021. "HMM-based adaptive attack-resilient control for Markov jump system and application to an aircraft model," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
    6. Fan, Zhencheng, 2017. "Convergence of numerical solutions to stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 176-187.
    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. Fan, Zhencheng, 2017. "Convergence of numerical solutions to stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 176-187.
    2. E. K. Boukas, 2004. "Nonfragile Controller Design for Linear Markovian Jumping Parameters Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 241-255, August.
    3. Dwueng-Chwuan Jhwueng, 2021. "Two Gaussian Bridge Processes for Mapping Continuous Trait Evolution along Phylogenetic Trees," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    4. Yang Li & Yaolei Wang & Taitao Feng & Yifei Xin, 2021. "A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps," Mathematics, MDPI, vol. 9(3), pages 1-14, January.
    5. Guillermo Andrés Cangrejo Jiménez, 2014. "La Estructura a Plazos del Riesgo Interbancario," Documentos de Trabajo 12172, Universidad del Rosario.
    6. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    7. Mao, Xuerong & Shen, Yi & Yuan, Chenggui, 2008. "Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1385-1406, August.
    8. Xi, Fubao, 2004. "Stability of a random diffusion with nonlinear drift," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 273-286, July.
    9. Fred Espen Benth & Paul Krühner, 2018. "Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models," Finance and Stochastics, Springer, vol. 22(2), pages 327-366, April.
    10. Jan Baldeaux & Fung & Katja Ignatieva & Eckhard Platen, 2015. "A Hybrid Model for Pricing and Hedging of Long-dated Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(4), pages 366-398, September.
    11. de la Cruz, H. & Jimenez, J. C, 2020. "Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    12. Gao, Xiangyu & Liu, Yi & Wang, Yanxia & Yang, Hongfu & Yang, Maosong, 2021. "Tamed-Euler method for nonlinear switching diffusion systems with locally Hölder diffusion coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    13. Yuan, Chenggui & Mao, Xuerong, 2004. "Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 223-235.
    14. Xu, Jiang & Chen, Tao & Wen, Xiangdan, 2021. "Analysis of a Bailey–Dietz model for vector-borne disease under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    15. Zhou, Qi & Yao, Deyin & Wang, Jiahui & Wu, Chengwei, 2016. "Robust control of uncertain semi-Markovian jump systems using sliding mode control method," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 72-87.
    16. Kevin Fergusson & Eckhard Platen, 2014. "Hedging long-dated interest rate derivatives for Australian pension funds and life insurers," Published Paper Series 2014-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    17. Andrew Papanicolaou, 2014. "Stochastic Analysis Seminar on Filtering Theory," Papers 1406.1936, arXiv.org, revised Oct 2016.
    18. Ye, Zhiyong & Zhang, He & Zhang, Hongyu & Zhang, Hua & Lu, Guichen, 2015. "Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 156-165.
    19. Mike Giles & Lukasz Szpruch, 2012. "Multilevel Monte Carlo methods for applications in finance," Papers 1212.1377, arXiv.org.
    20. Ma, Yuechao & Chen, Hui, 2015. "Reliable finite-time H∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 897-915.

    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:gam:jmathe:v:9:y:2021:i:6:p:588-:d:514106. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.