IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v353y2019icp166-177.html
   My bibliography  Save this article

Numerical analysis of the balanced implicit method for stochastic age-dependent capital system with poisson jumps

Author

Listed:
  • Kang, Ting
  • Li, Qiang
  • Zhang, Qimin

Abstract

The aim of this paper is to construct a numerical method to preserve positivity and mean-square dissipativity of stochastic age-dependent capital system with Poisson jumps. We use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution. It is proved that the balanced implicit method(BIM) preserves positivity and converges with order 12 under given conditions. In addition, some sufficient conditions are obtained for ensuring the system and the balanced implicit method(BIM) are mean-square dissipative. Finally, a numerical example is simulated to illustrate the efficiency of theoretical results.

Suggested Citation

  • Kang, Ting & Li, Qiang & Zhang, Qimin, 2019. "Numerical analysis of the balanced implicit method for stochastic age-dependent capital system with poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 166-177.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:166-177
    DOI: 10.1016/j.amc.2018.10.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318309202
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.10.054?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. Kahl Christian & Schurz Henri, 2006. "Balanced Milstein Methods for Ordinary SDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 12(2), pages 143-170, April.
    2. Tan, Jianguo & Men, Weiwei & Pei, Yongzhen & Guo, Yongfeng, 2017. "Construction of positivity preserving numerical method for stochastic age-dependent population equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 57-64.
    3. G. N. Milstein & Eckhard Platen & H. Schurz, 1998. "Balanced Implicit Methods for Stiff Stochastic Systems," Published Paper Series 1998-1, 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. Song, Bo & Zhang, Ya & Park, Ju H., 2021. "H∞ control for Poisson-driven stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 392(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. Li, Yan & Zhang, Qimin, 2020. "The balanced implicit method of preserving positivity for the stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Xiaoling Wang & Xiaofei Guan & Pei Yin, 2020. "A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations," Mathematics, MDPI, vol. 8(2), pages 1-17, February.
    3. Xianming Sun & Siqing Gan, 2014. "An Efficient Semi-Analytical Simulation for the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 43(4), pages 433-445, April.
    4. Halidias Nikolaos, 2016. "On the construction of boundary preserving numerical schemes," Monte Carlo Methods and Applications, De Gruyter, vol. 22(4), pages 277-289, December.
    5. Nikolaos Halidias & Ioannis Stamatiou, 2015. "Approximating explicitly the mean reverting CEV process," Papers 1502.03018, arXiv.org, revised May 2015.
    6. 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, July-Dece.
    7. H. A. Mardones & C. M. Mora, 2020. "First-Order Weak Balanced Schemes for Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 833-852, June.
    8. Tan, Jianguo & Men, Weiwei & Pei, Yongzhen & Guo, Yongfeng, 2017. "Construction of positivity preserving numerical method for stochastic age-dependent population equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 57-64.
    9. Yao, Jinran & Gan, Siqing, 2018. "Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 294-301.
    10. 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.
    11. Tan, Jianguo & Chen, Yang & Men, Weiwei & Guo, Yongfeng, 2021. "Positivity and convergence of the balanced implicit method for the nonlinear jump-extended CIR model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 195-210.
    12. Nikolaos Halidias, 2016. "On construction of boundary preserving numerical schemes," Papers 1601.07864, arXiv.org, revised Feb 2016.
    13. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    14. 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.
    15. 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.
    16. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013.
    17. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
    18. Zhang, Mengqing & Zhang, Qimin, 2019. "A positivity preserving numerical method for stochastic R&D model," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 193-203.
    19. Liu, Yufen & Cao, Wanrong & Li, Yuelin, 2022. "Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    20. Zhenyu Wang & Qiang Ma & Xiaohua Ding, 2020. "Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods," Mathematics, MDPI, vol. 8(12), pages 1-15, 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:353:y:2019:i:c:p:166-177. 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.