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BSDEs were first introduced by Pardoux and Peng in 1990 and have since become essential tools in [[stochastic control]] and [[financial mathematics]]. In the 1990s, [[Étienne Pardoux]] and [[Shige Peng]] established the existence and uniqueness theory for BSDE solutions, applying BSDEs to financial mathematics and control theory. For instance, BSDEs have been widely used in option pricing, risk measurement, and dynamic hedging<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>.
===Deep learning===
[[File:35c3-9386-eng-deu-Introduction to Deep Learning webm-hd.webm|35c3-9386-eng-deu-Introduction_to_Deep_Learning_webm-hd|upright=1.35]]
[[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<ref name="NatureBengio">{{cite journal |last1=LeCun |first1= Yann|last2=Bengio |first2=Yoshua | last3=Hinton | first3= Geoffrey|s2cid=3074096 |year=2015 |title=Deep Learning |journal=Nature |volume=521 |issue=7553 |pages=436–444 |doi=10.1038/nature14539 |pmid=26017442|bibcode=2015Natur.521..436L |url= https://hal.science/hal-04206682/file/Lecun2015.pdf}}</ref>.
===Limitations of Traditional Numerical Methods===
Tranditional numerical methods for solving stochastic differential equations<ref name="kloeden">Kloeden, P.E., Platen E. (1992). Numerical Solution of Stochastic Differential Equations. Springer, Berlin, Heidelberg. DOI: https://doi.org/10.1007/978-3-662-12616-5</ref> include the [[Euler–Maruyama method]], [[Milstein method]], [[Runge–Kutta method (SDE)]] and methods based on different representations of iterated stochastic integrals.<ref name="Kuznetsov">Kuznetsov, D.F. (2023). Strong approximation of iterated Itô and Stratonovich stochastic integrals: Method of generalized multiple Fourier series. Application to numerical integration of Itô SDEs and semilinear SPDEs. Differ. Uravn. Protsesy Upr., no. 1. DOI: https://doi.org/10.21638/11701/spbu35.2023.110</ref><ref name="Rybakov">Rybakov, K.A. (2023). Spectral representations of iterated stochastic integrals and their application for modeling nonlinear stochastic dynamics. Mathematics, vol. 11, 4047. DOI: https://doi.org/10.3390/math11194047</ref>
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