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On the MS-stability of predictor–corrector schemes for stochastic differential equations

Author

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  • Tocino, A.
  • Zeghdane, R.
  • Senosiaín, M.J.

Abstract

Predictor–corrector schemes are designed to be a compromise to retain the stability properties of the implicit schemes and the computational efficiency of the explicit ones. In this paper a complete analytical study for the linear mean-square stability of the two-parameter family of Euler predictor–corrector schemes for scalar stochastic differential equations is given. The analyzed family is given in terms of two parameters that control the degree of implicitness of the method. For each selection of the parameters the stability region is obtained, letting its comparison. Particular cases of the counter-intuitive fact of losing numerical stability by reducing the step size, is confirmed and proved. Figures of the MS-stability regions and numerical examples that confirm the theoretical results are shown.

Suggested Citation

  • Tocino, A. & Zeghdane, R. & Senosiaín, M.J., 2021. "On the MS-stability of predictor–corrector schemes for stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 289-305.
    • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:289-305
    DOI: 10.1016/j.matcom.2020.09.004
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    References listed on IDEAS

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    1. Buckwar, Evelyn & Sickenberger, Thorsten, 2011. "A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1110-1127.
    2. Eckhard Platen & Lei Shi, 2013. "On the numerical stability of simulation methods for SDEs under multiplicative noise in finance," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 183-194, January.
    3. Nicola Bruti-Liberati & Eckhard Platen, 2008. "Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations," Research Paper Series 222, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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