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<p>In this paper, we consider a fixed delay CIR process with Poisson jumps, which serves as an extended model proposed by [Stoch. Anal. Appl., 2019, 37(4): 550–573]. We rigorously present the existence, uniqueness and nonnegativeness of the exact solution. Furthermore, we develop a backward Euler–Maruyama (EM) method for the fixed delay model and show that the numerical solution converges strongly to the exact solution with rate <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({1\over 2}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Convergence Rate for a CIR Model with Fixed Delay Driven by Poisson Jumps

  • 期刊论文

  • 发表日期：

    2026年7月5日

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  • Shengrong Wang,
  • Jie Xie,
  • Li Tan

摘要

In this paper, we consider a fixed delay CIR process with Poisson jumps, which serves as an extended model proposed by [Stoch. Anal. Appl., 2019, 37(4): 550–573]. We rigorously present the existence, uniqueness and nonnegativeness of the exact solution. Furthermore, we develop a backward Euler–Maruyama (EM) method for the fixed delay model and show that the numerical solution converges strongly to the exact solution with rate \({1\over 2}\) 1 2 .