Error expansion for the discretization of backward stochastic differential equations

Emmanuel Gobet and Céline Labart

Stochastic Processes and their Applications, 2007, vol. 117, issue 7, 803-829

Abstract: We study the error induced by the time discretization of decoupled forward-backward stochastic differential equations (X,Y,Z). The forward component X is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XN with N time steps. The backward component is approximated by a backward scheme. Firstly, we prove that the errors (YN-Y,ZN-Z) measured in the strong Lp-sense (p>=1) are of order N-1/2 (this generalizes the results by Zhang [J. Zhang, A numerical scheme for BSDEs, The Annals of Applied Probability 14 (1) (2004) 459-488]). Secondly, an error expansion is derived: surprisingly, the first term is proportional to XN-X while residual terms are of order N-1.

Keywords: Backward; stochastic; differential; equation; Discretization; scheme; Malliavin; calculus; Semi-linear; parabolic; PDE (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (15)

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