Numerical Stability Analysis of the Euler Scheme for BSDEs

Abstract

In this paper, we study the qualitative behavior 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 cases 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.

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