Linear multi-step schemes for BSDEs

Abstract

We study the convergence rate of a class of linear multi-step methods for BSDEs. We show that, under a sufficient condition on the coefficients, the schemes enjoy a fundamental stability property. Coupling this result to an analysis of the truncation error allows us to design approximation with arbitrary order of convergence. Contrary to the analysis performed in \cite{zhazha10}, we consider general diffusion model and BSDEs with driver depending on $z$. The class of methods we consider contains well known methods from the ODE framework as Nystrom, Milne or Adams methods. We also study a class of Predictor-Correctot methods based on Adams methods. Finally, we provide a numerical illustration of the convergence of some methods.

30 pages, 2 figures

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