Numerical approximation of BSDEs with polynomial growth driver

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• Arnaud Lionnet (University of Birmingham)
• Wednesday 27 February 2019, 12:00-13:00
• Room R17/18, Watson building.

If you have a question about this talk, please contact Sergey Sergeev.

Backward Stochastic Differential Equations (BSDEs) provide a systematic way to obtain Feynman—Kac formulas for linear as well as nonlinear partial differential equations (PDEs) of parabolic and elliptic type, and the numerical approximation of their solutions thus provide Monte-Carlo methods for PDEs. BSD Es are also used to describe the solution of path-dependent stochastic control problems, and they further arise in many areas of mathematical finance.

In this talk, I will discuss the numerical approximation of BSD Es when the nonlinear driver is not Lipschitz, but instead has polynomial growth and satisfies a monotonicity condition. The time-discretization is a crucial step, as it determines whether the full numerical scheme is stable or not. Unlike for Lipschitz driver, while the implicit Bouchard—Touzi—Zhang scheme is stable, the explicit one is not and explodes in general. I will then present a number of remedies that allow to recover a stable scheme, while benefiting from the reduced computational cost of an explicit scheme. I will also discuss the issue of numerical stability and the qualitative correctness which is enjoyed by both the implicit scheme and the modified explicit schemes. Finally, I will discuss the approximation of the expectations involved in the full numerical scheme, and their analysis when using a quasi-Monte Carlo method.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

This talk is included in these lists:

• Optimisation and Numerical Analysis Seminars
• Room R17/18, Watson building
• School of Mathematics events

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