Discrete-time approximation of decoupled Forward-Backward SDE with jumps
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.
Year of publication: |
2008
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Authors: | Bouchard, Bruno ; Elie, Romuald |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 118.2008, 1, p. 53-75
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Publisher: |
Elsevier |
Keywords: | Discrete-time approximation Forward-Backward SDEs with jumps Malliavin calculus |
Saved in:
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