Fetching the paper…
Reading the bibliography…
A novel discretization is presented for forward-backward stochastic differential equations (FBSDE) with differentiable coefficients, simultaneously solving the BSDE and its Malliavin sensitivity problem.
“Approximation by superpositions of a sigmoidal function” Publisher: Springer
George Cybenko · 1989
Earlier work this paper cites.
“Approximation capabilities of multilayer feedforward networks”
Kurt Hornik · 1991
Earlier work this paper cites.
“Numerical Solution of Stochastic Differential Equations”
Peter Kloeden and Eckhard Platen · 1992
Earlier work this paper cites.
“Backward stochastic differential equations and quasilinear parabolic partial differential equations”
E. Pardoux and S. Peng · 1992
Earlier work this paper cites.
“Solving forward-backward stochastic differential equations explicitly — a four step scheme”
Jin Ma, Philip Protter and Jiongmin Yong · 1994
Earlier work this paper cites.
“Backward stochastic differential equations in finance” Publisher: Wiley Online Library
Nicole El, Shige Peng and Marie Quenez · 1997
Earlier work this paper cites.
“Brownian Motion and Stochastic Calculus”, Graduate Texts in Mathematics
Ioannis Karatzas and Steven Shreve · 1998
Earlier work this paper cites.
“Approximation theory of the MLP model in neural networks” Publisher: Cambridge University Press
Allan Pinkus · 1999
Earlier work this paper cites.
“Representation theorems for backward stochastic differential equations” Publisher: The Institute of Mathematical Statistics
Jin Ma and Jianfeng Zhang · 2002
Earlier work this paper cites.
“A quantization algorithm for solving multidimensional discrete-time optimal stopping problems” Publisher: Bernoulli Society for Mathematical Statistics and Probability
Vlad Bally and Gilles Pagès · 2003
Earlier work this paper cites.
“Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations”
Bruno Bouchard and Nizar Touzi · 2004
Earlier work this paper cites.
“A numerical scheme for BSDEs” Publisher: The Institute of Mathematical Statistics
Jianfeng Zhang · 2004
Earlier work this paper cites.
“A regression-based Monte Carlo method to solve backward stochastic differential equations” Publisher: The Institute of Mathematical Statistics
Emmanuel Gobet, Jean-Philippe Lemor and Xavier Warin · 2005
Earlier work this paper cites.
“A forward - Backward stochastic algorithm for quasi-linear PDES”
François Delarue and Stéphane Menozzi · 2006
Earlier work this paper cites.
“Approximation error analysis of some deep backward schemes for nonlinear PDEs” arXiv: 2006.01496
Maximilien Germain, Huyen Pham and Xavier Warin · 2006
Earlier work this paper cites.
“Spectral residual method without gradient information for solving large-scale nonlinear systems of equations”
William La, José Martínez and Marcos Raydan · 2006
Cited alongside, same era.
“Numerical Algorithms for Forward-Backward Stochastic Differential Equations” Publisher: Society for Industrial and Applied Mathematics
G.. Milstein and M.. Tretyakov · 2006
Cited alongside, same era.
“The Malliavin Calculus and Related Topics”, Probability and Its Applications
David Nualart · 2006
Cited alongside, same era.
“A forward scheme for backward SDEs”
Christian Bender and Robert Denk · 2007
Cited alongside, same era.
“Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs”
Patrick Cheridito, H. Soner, Nizar Touzi and Nicolas Victoir · 2007
Cited alongside, same era.
“Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance”
M.. Ruijter and C.. Oosterlee · 2015
Later among the works it cites.
“Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions” Publisher: The Institute of Mathematical Statistics and the Bernoulli Society
Plamen Turkedjiev · 2015
Later among the works it cites.
“Layer Normalization” arXiv: 1607.06450
Jimmy Ba, Jamie Kiros and Geoffrey. Hinton · 2016
Later among the works it cites.
“Numerical simulation of quadratic BSDEs” Publisher: Institute of Mathematical Statistics
Jean-François Chassagneux and Adrien Richou · 2016
Later among the works it cites.
“Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations”
E Gobet and P Turkedjiev · 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
“A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions” Publisher: Society for Industrial and Applied Mathematics
F. Fang and C.. Oosterlee · 2009
Cited alongside, same era.
“Path regularity and explicit convergence rate for BSDE with truncated quadratic growth”
Peter Imkeller and Gonçalo Dos · 2009
Cited alongside, same era.
“Understanding the difficulty of training deep feedforward neural networks” ISSN: 1938-7228
Xavier Glorot and Yoshua Bengio · 2010
Cited alongside, same era.
“A probabilistic numerical method for fully nonlinear parabolic PDEs” Publisher: Institute of Mathematical Statistics
Arash Fahim, Nizar Touzi and Xavier Warin · 2011
Cited alongside, same era.
“Malliavin calculus for backward stochastic differential equations and application to numerical solutions” Publisher: The Institute of Mathematical Statistics
Yaozhong Hu, David Nualart and Xiaoming Song · 2011
Cited alongside, same era.
“Least-Squares Monte Carlo for Backward SDEs”
Christian Bender and Jessica Steiner · 2012
Cited alongside, same era.
“Reducing variance in the numerical solution of BSDEs”
Samu Alanko and Marco Avellaneda · 2013
Cited alongside, same era.
Later among the works it cites.
“Deep Learning”
Ian Goodfellow, Yoshua Bengio and Aaron Courville · 2016
Later among the works it cites.
“On the Malliavin differentiability of BSDEs” Publisher: Institut Henri Poincaré
Thibaut Mastrolia, Dylan Possamaï and Anthony Réveillac · 2017
Later among the works it cites.
“Solving high-dimensional partial differential equations using deep learning” Publisher: National Academy of Sciences
Jiequn Han, Arnulf Jentzen and Weinan E · 2018
Later among the works it cites.
“Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations”
Christian Beck, E. Weinan and Arnulf Jentzen · 2019
Later among the works it cites.
“Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs”
Masaaki Fujii, Akihiko Takahashi and Masayuki Takahashi · 2019
Later among the works it cites.
“Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions”
Yangang Chen and Justin.. Wan · 2020
Later among the works it cites.
“Convergence of the deep BSDE method for coupled FBSDEs” Publisher: Springer
Jiequn Han and Jihao Long · 2020
Later among the works it cites.
“Deep backward schemes for high-dimensional nonlinear PDEs”
Côme Huré, Huyên Pham and Xavier Warin · 2020
Later among the works it cites.
“Strong error analysis for stochastic gradient descent optimization algorithms”
Arnulf Jentzen, Benno Kuckuck, Ariel Neufeld and Philippe von Wurstemberger · 2021
Closest in time.