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Discrete-time approximation of decoupled Forward-Backward SDE with jumps

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  • Bouchard, Bruno
  • Elie, Romuald

Abstract

We study a discrete-time approximation for solutions of systems of decoupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps. Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the number of time steps n goes to infinity. The rate of convergence is at least n-1/2+[epsilon], for any [epsilon]>0. When the jump coefficient of the first variation process of the forward component satisfies a non-degeneracy condition which ensures its inversibility, we achieve the optimal convergence rate n-1/2. The proof is based on a generalization of a remarkable result on the path-regularity of the solution of the backward equation derived by Zhang [J. Zhang, A numerical scheme for BSDEs, Annals of Applied Probability 14 (1) (2004) 459-488] in the no-jump case.

Suggested Citation

  • Bouchard, Bruno & Elie, Romuald, 2008. "Discrete-time approximation of decoupled Forward-Backward SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 53-75, January.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:1:p:53-75
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    References listed on IDEAS

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    1. Anne Eyraud-Loisel, 2005. "Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps," Post-Print hal-01298905, HAL.
    2. 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.
    3. 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.
    4. Buckdahn, R. & Pardoux, E., 1994. "BSDE's with jumps and associated integro-partial differential equations," SFB 373 Discussion Papers 1994,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Eyraud-Loisel, Anne, 2005. "Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1745-1763, November.
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