# Error expansion for the discretization of Backward Stochastic Differential Equations

2 MATHFI - Mathématiques financières
LJK - Laboratoire Jean Kuntzmann
Abstract : We study the error induced by the time discretization of a 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 $X^N$ with $N$ time steps. The backward component is approximated by a backward scheme. Firstly, we prove that the errors $(Y^N-Y,Z^N-Z)$ measured in the strong $L_p$-sense ($p \geq 1$) are of order $N^{-1/2}$ (this generalizes the results by Zhang 2004). Secondly, an error expansion is derived: surprisingly, the first term is proportional to $X^N-X$ while residual terms are of order $N^{-1}$.
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Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-00019463
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Submitted on : Wednesday, February 22, 2006 - 3:08:21 PM
Last modification on : Wednesday, October 20, 2021 - 12:24:01 AM
Long-term archiving on: : Saturday, April 3, 2010 - 10:32:48 PM

### Citation

Emmanuel Gobet, Céline Labart. Error expansion for the discretization of Backward Stochastic Differential Equations. Stochastic Processes and their Applications, Elsevier, 2007, 117 (7), pp.803-829. ⟨10.1016/j.spa.2006.10.007⟩. ⟨hal-00019463⟩

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