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

Bruno Bouchard and Romuald Elie

Stochastic Processes and their Applications, 2008, vol. 118, issue 1, 53-75

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.

Keywords: Discrete-time; approximation; Forward-Backward; SDEs; with; jumps; Malliavin; calculus (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (37)

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