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'''Deep BSDE''' (Deep Backward Stochastic Differential Equation) is a numerical method that combines [[deep learning]] with [[Backward stochastic differential equation]] (BSDE). This method is particularly useful for solving high-dimensional problems in [[financial derivatives]] pricing and [[risk management]]. By leveraging the powerful function approximation capabilities of [[deep neural networks]], deep BSDE addresses the computational challenges faced by traditional numerical methods in high-dimensional settings <ref name="Han2018">{{cite journal | last1=Han | first1=J. | last2=Jentzen | first2=A. | last3=E | first3=W. | title=Solving high-dimensional partial differential equations using deep learning | journal=Proceedings of the National Academy of Sciences | volume=115 | issue=34 | pages=8505-8510 | year=2018 }}</ref>.
==History==
Backward stochastic differential equations were introduced by [[Jean-Michel Bismut]] in 1973 in the linear case<ref>{{cite journal|last=Bismut|first=Jean-Michel|year=1973|title=Conjugate convex functions in optimal stochastic control|journal=Journal of Mathematical Analysis and Applications|volume=44|issue=2 |pages=384–404|doi=10.1016/0022-247X(73)90066-8}}</ref> . In the 1990s, [[Étienne Pardoux]] and [[Shige Peng]] established the existence and uniqueness theory for nonlinear BSDE solutions, applying BSDEs to financial mathematics and control theory<ref name="Pardoux1990">{{cite journal | last1=Pardoux | first1=E. | last2=Peng | first2=S. | title=Adapted solution of a backward stochastic differential equation | journal=Systems & Control Letters | volume=14 | issue=1 | pages=55-61 | year=1990 }}</ref>. For instance, BSDEs have been widely used in option pricing, risk measurement, and dynamic hedging.
[[Deep Learning]] is a [[machine learning]] method based on multilayer [[neural networks]]. Its core concept can be traced back to the neural computing models of the 1940s. In the 1980s, the proposal of the [[backpropagation]] algorithm made the training of multilayer neural networks possible. In 2006, the [[Deep Belief Networks]] proposed by [[Geoffrey Hinton]] and others rekindled interest in deep learning. Since then, deep learning has made groundbreaking advancements in [[image processing]], [[speech recognition]], [[natural language processing]], and other fields.
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