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Article Dans Une Revue Stochastic Processes and their Applications Année : 2008

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

Résumé

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+ε, for any ε>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.
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Dates et versions

hal-00362300 , version 1 (17-02-2009)

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  • HAL Id : hal-00362300 , version 1

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Bruno Bouchard, Romuald Elie. Discrete-time approximation of decoupled Forward–Backward SDE with jumps. Stochastic Processes and their Applications, 2008, 118 (1), pp.53-75. ⟨hal-00362300⟩
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