Numerical stability analysis of the Euler scheme for BSDEs

Jean-François Chassagneux; Adrien Richou

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arXiv · 1407.0887

Numerical stability analysis of the Euler scheme for BSDEs

Jean-François Chassagneux·Adrien Richou

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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.

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BibTeX RIS

Jean-François Chassagneux, Adrien Richou. 2014-07-03. Numerical stability analysis of the Euler scheme for BSDEs. https://arxiv.org/abs/1407.0887

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