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Adapted $\theta$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations

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  • Chol-Kyu Pak
  • Mun-Chol Kim
  • Chang-Ho Rim

Abstract

In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $\theta$-scheme, we reduce truncation errors by taking $\theta$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear scheme and verify the order of scheme through a typical numerical experiment.

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  • Chol-Kyu Pak & Mun-Chol Kim & Chang-Ho Rim, 2018. "Adapted $\theta$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations," Papers 1808.02173, arXiv.org.
  • Handle: RePEc:arx:papers:1808.02173
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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.
    3. Gobet, Emmanuel & Labart, Céline, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.
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