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One order numerical scheme for forward–backward stochastic differential equations

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  • Gong, Benxue
  • Rui, Hongxing

Abstract

A one order numerical scheme based on the four step scheme developed by Ma et al. for the adapted solutions to a class of forward–backward stochastic differential equations is proposed and analyzed. For the decoupling quasilinear parabolic equations, a new kind of characteristics and finite difference method is used. While for the decoupled forward SDE, we use the Milstein scheme.

Suggested Citation

  • Gong, Benxue & Rui, Hongxing, 2015. "One order numerical scheme for forward–backward stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 220-231.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:220-231
    DOI: 10.1016/j.amc.2015.08.127
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    References listed on IDEAS

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    1. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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    Cited by:

    1. Pelsser Antoon & Gnameho Kossi, 2019. "A Monte Carlo method for backward stochastic differential equations with Hermite martingales," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 37-60, March.
    2. Gnameho Kossi & Stadje Mitja & Pelsser Antoon, 2024. "A gradient method for high-dimensional BSDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 30(2), pages 183-203.

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