Discrete-time approximation of decoupled Forward–Backward SDE with jumps
Bouchard, Bruno; Elie, Romuald (2008), Discrete-time approximation of decoupled Forward–Backward SDE with jumps, Stochastic Processes and their Applications, 118, 1, p. 53-75. http://dx.doi.org/10.1016/j.spa.2007.03.010
TypeArticle accepté pour publication ou publié
Journal nameStochastic Processes and their Applications
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Abstract (EN)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.
Subjects / KeywordsDiscrete-time approximation; Forward–Backward SDEs with jumps; Malliavin calculus
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