Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

Solving the quantum many-body problem with artificial neural networks

(2017) Giuseppe Carleo et al.   SCIENCE

Numerical simulation of quadratic BSDEs

(2016) Jean-François Chassagneux et al.   ANNALS OF APPLIED PROBABILITY

Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance

(2016) M.J. Ruijter et al.   APPLIED NUMERICAL MATHEMATICS

Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression

(2016) Emmanuel Gobet et al.   BERNOULLI

Efficient numerical Fourier methods for coupled forward–backward SDEs

(2016) T.P. Huijskens et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Mastering the game of Go with deep neural networks and tree search

(2016) David Silver et al.   NATURE

Stratified Regression Monte-Carlo Scheme for Semilinear PDEs and BSDEs with Large Scale Parallelization on GPUs

(2016) E. Gobet et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Simulation of BSDEs with jumps by Wiener Chaos expansion

(2016) Christel Geiss et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Time discretization of FBSDE with polynomial growth drivers and reaction–diffusion PDEs

(2015) Arnaud Lionnet et al.   ANNALS OF APPLIED PROBABILITY

A monotone scheme for high-dimensional fully nonlinear PDEs

(2015) Wenjie Guo et al.   ANNALS OF APPLIED PROBABILITY

Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

(2015) Tao Kong et al.   Communications in Computational Physics

Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case

(2015) Dylan Possamaï et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

A PRIMAL-DUAL ALGORITHM FOR BSDES

(2015) Christian Bender et al.   MATHEMATICAL FINANCE

TRADING WITH SMALL PRICE IMPACT

(2015) Ludovic Moreau et al.   MATHEMATICAL FINANCE

Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions

(2015) Emmanuel Gobet et al.   MATHEMATICS OF COMPUTATION

Deep learning

(2015) Yann LeCun et al.   NATURE

Learning solutions to partial differential equations using LS-SVM

(2015) Siamak Mehrkanoon et al.   NEUROCOMPUTING

Numerical Stability Analysis of the Euler Scheme for BSDEs

(2015) Jean-François Chassagneux et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs

(2015) M. J. Ruijter et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Simulation of BSDEs by Wiener chaos expansion

(2014) Philippe Briand et al.   ANNALS OF APPLIED PROBABILITY

Runge–Kutta schemes for backward stochastic differential equations

(2014) Jean-François Chassagneux et al.   ANNALS OF APPLIED PROBABILITY

Second order discretization of backward SDEs and simulation with the cubature method

(2014) Dan Crisan et al.   ANNALS OF APPLIED PROBABILITY

Linear Multistep Schemes for BSDEs

(2014) Jean-François Chassagneux   SIAM JOURNAL ON NUMERICAL ANALYSIS

A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations

(2013) Guannan Zhang et al.   JOURNAL OF COMPUTATIONAL MATHEMATICS

A numerical algorithm for a class of BSDEs via the branching process

(2013) Pierre Henry-Labordère et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

A review of numerical methods for nonlinear partial differential equations

(2012) Eitan Tadmor   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups

(2012) Geoffrey Hinton et al.   IEEE SIGNAL PROCESSING MAGAZINE

Solving Backward Stochastic Differential Equations Using the Cubature Method: Application to Nonlinear Pricing

(2012) D. Crisan et al.   SIAM Journal on Financial Mathematics

A probabilistic numerical method for fully nonlinear parabolic PDEs

(2011) Arash Fahim et al.   ANNALS OF APPLIED PROBABILITY

Probabilistic methods for semilinear partial differential equations. Applications to finance

(2010) Dan Crisan et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation

(2010) A. Rasulov et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

Solving BSDE with Adaptive Control Variate

(2010) Emmanuel Gobet et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights

(2010) D. Crisan et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques

(2008) Mehdi Dehghan et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS