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Convergence of the Euler–Maruyama method for CIR model with Markovian switching

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  • Zhang, Zhenzhong
  • Zhou, Tiandao
  • Jin, Xinghu
  • Tong, Jinying

Abstract

In this paper, we focus on the convergence of stochastic differential equations with Markovian switching and 1∕2-Hölder continuous diffusion coefficients. We give the convergence between numerical solutions and explicit solutions at a rate of 1∕logn by the Euler–Maruyama method. Parameter estimations for CIR model with Markovian switching are obtained by the quadratic variation method and composite likelihood method.

Suggested Citation

  • Zhang, Zhenzhong & Zhou, Tiandao & Jin, Xinghu & Tong, Jinying, 2020. "Convergence of the Euler–Maruyama method for CIR model with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 192-210.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:192-210
    DOI: 10.1016/j.matcom.2020.04.013
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    3. 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.
    4. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
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