Discrete time approximation of decoupled Forward-Backward SDE with jumps

By Bruno Bouchard, Romuald Elie. 2008

183 citations recorded by the source corpus.

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+e, for any e>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.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e16220f7a75e2937e6ab2bbdd0405ec5c45980f9

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Citations in the corpus

RUNGE-KUTTA SCHEMES FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS (2014, methodology): “These schemes are based on the well-known Runge–Kutta methods for ODEs and include new high order schemes as well as existing low order schemes such as the classical extension of the Euler scheme to BSDEs; see, for example, [1, 2, 4, 6].”
On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights (2010, methodology): “In contrast with the above literature, we concenrate on approximations of solutions of backward stochastic differential equations based on the Monte Carlo simulation of the underlying Brownian motion, thus continuing the studies of Bouchard and Touzi [6], Zhang [18] and Gobet, Lemor and Warin [9].”
A stochastic target formulation for optimal switching problems in finite horizon (2009, background): “To conclude this introduction, we would like to observe that our representation of variational PDEs by stochastic target problems is in the spirit of [18] where systems of quasi-linear PDEs are related to Backward SDEs with jumps, see also [14] and [3] for numerical applications.”
Least-Squares Monte Carlo for Backward SDEs (2012, methodology): “For a time discretization scheme of BSDEs with jumps under Lipschitz conditions we refer to Bouchard and Elie (2008).”
About the Pricing Equations in Finance (2011, unknown): “Bouchard and Elie [27]).”
Discrete-time approximation for continuously and discretely reflected BSDEs (2008, background): “In the non-re ected case, such approximations have been studied by [3] and [16], see also [2] and [6] for BSDEs with jumps.”