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Tamed-Euler method for nonlinear switching diffusion systems with locally Hölder diffusion coefficients

Author

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  • Gao, Xiangyu
  • Liu, Yi
  • Wang, Yanxia
  • Yang, Hongfu
  • Yang, Maosong

Abstract

It is widely known that stochastic differential equations with Markovian switching, involving terms without Lipschitz continuity like |u|1/2+α for α∈[0,1/2), are of great practical value in many fields such as finance and biology. In this paper, we develop the tamed Euler-Maruyama schemes for switching diffusion systems modulated by a Markov chain, under the circumstances that drift coefficient satisfies the locally Lipschitz condition and diffusion coefficient satisfies the locally Hölder continuous condition. Moreover, we obtain the rate of convergence of the numerical algorithm not only at time T but also over the time interval [0,T]. Finally we give the numerical experiments to illustrate the theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921005786
    DOI: 10.1016/j.chaos.2021.111224
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    References listed on IDEAS

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    1. Ngo, Hoang Long & Luong, Duc Trong, 2019. "Tamed Euler–Maruyama approximation for stochastic differential equations with locally Hölder continuous diffusion coefficients," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 133-140.
    2. 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.
    3. Longstaff, Francis A., 1989. "A nonlinear general equilibrium model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 23(2), pages 195-224, August.
    4. Ngo, Hoang-Long & Taguchi, Dai, 2017. "Strong convergence for the Euler–Maruyama approximation of stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 55-63.
    5. Choi Seungmoon, 2009. "Regime-Switching Univariate Diffusion Models of the Short-Term Interest Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(1), pages 1-41, March.
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