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This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs).
Deep-learning based numerical BSDE method for Barrier options
Yu, B., Xing, X., and Sudjianto, A. (2019) · 1904
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Introduction to solving quant finance problems with time-stepped FBSDE and deep learning
Hientzsch, B. (2019) · 1911
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Robust training and initialization of deep neural networks: An adaptive basis viewpoint
Cyr, E. C., Gulian, M. A., Patel, R. G., Perego, M., and Trask, N. A. (2019) · 1912
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Backward stochastic differential equations in finance
El Karoui, N., Peng, S., and Quenez, M. C. (1997) · 1997
Earlier work this paper cites.
Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order
Pardoux, É. (1998) · 1998
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BSDE driven by dirichlet process and semi-linear parabolic PDE. Application to homogenization
Lejay, A. (2002) · 2002
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On pricing of discrete barrier options
Kou, S. (2003) · 2003
Cited alongside, same era.
Stochastic Calculus for Finance II
Shreve, S. (2004) · 2004
Cited alongside, same era.
Kremsner, S., Steinicke, A., and Szölgyenyi, M. (2020) · 2010
Cited alongside, same era.
Backward Stochastic Differential Equations: An introduction
Perkowski, N. (2010) · 2010
Cited alongside, same era.
Bergman, Piterbarg, and beyond: Pricing derivatives under collateralization and differential rates
Mercurio, F. (2015) · 2015
Later among the works it cites.
Solving high-dimensional partial differential equations using deep learning
Han, J., Jentzen, A., and E, W. (2018) · 2018
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Raissi, M. (2018) · 2018
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Machine learning for semi linear PDEs
Chan-Wai-Nam, Q., Mikael, J., and Warin, X. (2019) · 2019
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Notes on stochastic finance
Privault, N. (2021) · 2021
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