Numerical stability analysis of the Euler scheme for BSDEs

Abstract

In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stability. We then perform a classical Von Neumann stability analysis in the case of a linear driver $f$ and exhibit necessary conditions to get stability in this case. Finally, we illustrate our results with numerical applications.

References in corpus (3)

• Numerical simulation of quadratic BSDEs
• Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs
• Linear multi-step schemes for BSDEs