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2020

Backward Deep BSDE Methods and Applications to Nonlinear Problems

Yu, Yajie, Hientzsch, Bernhard, Ganesan, Narayan

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In this paper, we present a backward deep BSDE method applied to Forward Backward Stochastic Differential Equations (FBSDE) with given terminal condition at maturity that time-steps the BSDE backwards.

We present an application of this method to a nonlinear pricing problem - the differential rates problem.
To time-step the BSDE backward, one needs to solve a nonlinear problem.
For the differential rates problem, we derive an exact solution of this time-step problem and a Taylor-based approximation.

Backward Deep BSDE Methods and Applications to Nonlinear Problems · Around

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Numerical methods for controlled hamilton-jacobi-bellman pdes in finance
Peter A Forsyth and George Labahn · 2007
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Bergman, Piterbarg, and beyond: pricing derivatives under collateralization and differential rates
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
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Weinan E, Jiequn Han, and Arnulf Jentzen · 2017
Earlier work this paper cites.
Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and Weinan E · 2018
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