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Positivity and convergence of the balanced implicit method for the nonlinear jump-extended CIR model

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  • Tan, Jianguo
  • Chen, Yang
  • Men, Weiwei
  • Guo, Yongfeng

Abstract

In this paper, we extend the balanced implicit method (BIM) to nonlinear jump-extended Cox–Ingersoll–Ross (CIR) model. Firstly, we construct the numerical method BIM for this nonlinear jump-extended CIR model and prove the positivity of the proposed method for the model. Furthermore the strong convergence of the BIM is proved in L1 and L2 sense. Finally, we give two examples to illustrate the positivity and convergence of the BIM; numerical results verify the theoretical findings.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:195-210
    DOI: 10.1016/j.matcom.2020.10.024
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    References listed on IDEAS

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    1. 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.
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    3. 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.
    4. Rathinasamy, Anandaraman & Nair, Priya, 2018. "Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 276-303.
    5. N. Halidias & I. S. Stamatiou, 2015. "Approximating Explicitly the Mean-Reverting CEV Process," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-20, November.
    6. Nikolaos Halidias & Ioannis Stamatiou, 2015. "Approximating explicitly the mean reverting CEV process," Papers 1502.03018, arXiv.org, revised May 2015.
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