Discrete time approximation of decoupled Forward-Backward SDE with jumps - Archive ouverte HAL Access content directly
Journal Articles Stochastic Processes and their Applications Year : 2008

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

Bruno Bouchard
• Function : Author
• PersonId : 1038139
Romuald Elie
• Function : Author

#### Abstract

We study a discrete-time approximation for solutions of systems of decoupled forward-backward stochastic differential equations 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. When the jump coefficient of the first variation process of the forward component satisfies a non-degeneracy condition which ensures its inversibility, we obtain 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 (2001, 2004) in the no-jump case. A similar result is obtained without the non-degeneracy assumption whenever the coefficients are $C^1_b$ with Lipschitz derivatives. Several extensions of these results are discussed. In particular, we propose a convergent scheme for the resolution of systems of coupled semilinear parabolic PDE's.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

hal-00015486 , version 1 (08-12-2005)

### Identifiers

• HAL Id : hal-00015486 , version 1

### Cite

Bruno Bouchard, Romuald Elie. Discrete time approximation of decoupled Forward-Backward SDE with jumps. Stochastic Processes and their Applications, 2008, 118 (1), pp.53-75. ⟨hal-00015486⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

161 View