Abstract
We demonstrate that the use of asymptotic expansion as prior knowledge in the “deep BSDE solver”, which is a deep learning method for high dimensional BSDEs proposed by Weinan et al. (Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, 2017b. ar**v:1706.04702), drastically reduces the loss function and accelerates the speed of convergence. We illustrate the technique and its implications by using Bergman’s model with different lending and borrowing rates as a typical model for FVA as well as a class of solvable BSDEs with quadratic growth drivers. We also present an extension of the deep BSDE solver for reflected BSDEs representing American option prices.
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The research is partially supported by Center for Advanced Research in Finance (CARF).
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Fujii, M., Takahashi, A. & Takahashi, M. Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs. Asia-Pac Financ Markets 26, 391–408 (2019). https://doi.org/10.1007/s10690-019-09271-7
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DOI: https://doi.org/10.1007/s10690-019-09271-7