Numerical methods for backward stochastic differential equations: a survey
From MaRDI portal
Publication:6158181
DOI10.1214/23-ps18zbMath1515.65023arXiv2101.08936MaRDI QIDQ6158181
Yuji Shinozaki, Jared Chessari, Toshihiro Yamada, Reiichiro Kawai
Publication date: 31 May 2023
Published in: Probability Surveys (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.08936
Malliavin calculusMonte Carlo methodsPicard iterationdeep learningleast-squares regressionsemilinear PDEs
Artificial neural networks and deep learning (68T07) Monte Carlo methods (65C05) Dynamic programming in optimal control and differential games (49L20) Optimal stochastic control (93E20) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Stochastic calculus of variations and the Malliavin calculus (60H07) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)
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Cites Work
- Cemracs 2017: numerical probabilistic approach to MFG
- Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view
- Data informed solution estimation for forward-backward stochastic differential equations
- Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation
- A polynomial scheme of asymptotic expansion for backward SDEs and option pricing
- Mean square rate of convergence for random walk approximation of forward-backward SDEs
- Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
- Approximation Error Analysis of Some Deep Backward Schemes for Nonlinear PDEs
- Approximation of BSDE with non Lipschitz coefficient
- Stochastic grid bundling method for backward stochastic differential equations
- Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations
- ADJOINT FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY JUMP DIFFUSION PROCESSES AND ITS APPLICATION TO NONLINEAR FILTERING PROBLEMS
- A High-Order Numerical Method for BSPDEs with Applications to Mathematical Finance
- Stability analysis of general multistep methods for Markovian backward stochastic differential equations
- Asymptotic expansion for forward-backward SDEs with jumps
- Uniform error estimates for artificial neural network approximations for heat equations
- Sinc-$\theta$ Schemes for Backward Stochastic Differential Equations
- A Multistep Scheme to Solve Backward Stochastic Differential Equations for Option Pricing on GPUs
- A Unified Probabilistic Discretization Scheme for FBSDEs: Stability, Consistency, and Convergence Analysis
- Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- A Fully Discrete Explicit Multistep Scheme for Solving Coupled Forward Backward Stochastic Differential Equations
- High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control
- Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
- Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences
- An Explicit Second-Order Numerical Scheme to Solve Decoupled Forward Backward Stochastic Equations
- Stability results for martingale representations: The general case
- Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing
- Linear Multistep Schemes for BSDEs
- Numerical Stability Analysis of the Euler Scheme for BSDEs
- A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs
- Central Clearing Valuation Adjustment
- Backward Stochastic Differential Equations
- A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations
- A PRIMAL–DUAL ALGORITHM FOR BSDES
- A New Kind of Accurate Numerical Method for Backward Stochastic Differential Equations
- COUNTERPARTY RISK AND FUNDING: THE FOUR WINGS OF THE TVA
- Importance Sampling for Backward SDEs
- Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation
- Prediction-Correction Scheme for Decoupled Forward Backward Stochastic Differential Equations with Jumps
- A Numerical Method and its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations
- Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs
- Explicit theta-Schemes for Mean-Field Backward Stochastic Differential Equations
- On the Starting and Stopping Problem: Application in Reversible Investments
- A Posteriori Estimates for Backward SDEs
- A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations
- An interpolated stochastic algorithm for quasi-linear PDEs
- Stability of solutions of BSDEs with random terminal time
- Numerical Algorithms for Forward-Backward Stochastic Differential Equations
- Branching Diffusion Processes
- Sequential Control Variates for Functionals of Markov Processes
- A Numerical Scheme for the Quantile Hedging Problem
- Convergence of a Robust Deep FBSDE Method for Stochastic Control
- A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
- Applications of Malliavin calculus to Monte-Carlo methods in finance. II
- Donsker-type theorem for BSDEs
- Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression
- Deep xVA Solver: A Neural Network–Based Counterparty Credit Risk Management Framework
- Approximations for adapted M-solutions of type-II backward stochastic Volterra integral equations
- Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance
- Numerical simulation of quadratic BSDEs
- Convergence of BS\(\operatorname{\Delta}\)Es driven by random walks to BSDEs: the case of (in)finite activity jumps with general driver
- Simulation of BSDEs with jumps by Wiener chaos expansion
- Numerical approximation of doubly reflected BSDEs with jumps and RCLL obstacles
- Counterparty risk and funding: immersion and beyond
- Backward stochastic differential equations with jumps and their actuarial and financial applications. BSDEs with jumps
- BS\(\Delta\)Es and BSDEs with non-Lipschitz drivers: comparison, convergence and robustness
- Forward-backward systems for expected utility maximization
- Generalized fractional smoothness and \(L_p\)-variation of BSDEs with non-Lipschitz terminal condition
- A generalized \(\theta\)-scheme for solving backward stochastic differential equations
- Discrete-time approximation of multidimensional BSDEs with oblique reflections
- Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations
- A convolution method for numerical solution of backward stochastic differential equations
- Adapted solution of a backward stochastic differential equation
- A parallel four step domain decomposition scheme for coupled forward-backward stochastic differential equations
- A probabilistic numerical method for fully nonlinear parabolic PDEs
- Numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers
- Numerical simulation of BSDEs with drivers of quadratic growth
- Malliavin calculus for backward stochastic differential equations and application to numerical solutions
- Backward stochastic differential equations with reflection and Dynkin games
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering
- Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs
- A new numerical method for 1-D backward stochastic differential equations without using conditional expectations
- Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
- The steepest descent method for forward-backward SDEs
- Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
- Error expansion for the discretization of backward stochastic differential equations
- Discretisation of FBSDEs driven by càdlàg martingales
- Efficient numerical Fourier methods for coupled forward-backward SDEs
- Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles
- Convergence of solutions of discrete reflected backward SDE's and simulations
- \(\mathbf L_2\)-time regularity of BSDEs with irregular terminal functions
- On the Monte Carlo simulation of BSDEs: an improvement on the Malliavin weights
- Error estimates of the \(\theta\)-scheme for backward stochastic differential equations
- Backward stochastic differential equations with constraints on the gains-process
- Hedging contingent claims with constrained portfolios
- Solving forward-backward stochastic differential equations explicitly -- a four step scheme
- Reflected solutions of backward SDE's, and related obstacle problems for PDE's
- Conjugate convex functions in optimal stochastic control
- A quantization algorithm for solving multidimensional discrete-time optimal stopping problems
- A numerical scheme for BSDEs
- Reflected BSDEs and mixed game problem
- Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth
- An asymptotic expansion for forward-backward SDEs: a Malliavin calculus approach
- On the homotopy analysis method for backward/forward-backward stochastic differential equations
- Numerical approximation of BSDEs using local polynomial drivers and branching processes
- Regularity of BSDEs with a convex constraint on the gains-process
- Nesting Monte Carlo for high-dimensional non-linear PDEs
- Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
- One order numerical scheme for forward-backward stochastic differential equations
- Sharp derivative bounds for solutions of degenerate semi-linear partial differential equations
- On the robustness of backward stochastic differential equations.
- Stability in \(\mathbb D\) of martingales and backward equations under discretization of filtration
- Discretizing a backward stochastic differential equation
- Representation theorems for backward stochastic differential equations
- Numerical method for backward stochastic differential equations
- Backward stochastic differential equations and partial differential equations with quadratic growth.
- On the Malliavin approach to Monte Carlo approximation of conditional expectations
- \(L^p\)-error estimates for numerical schemes for solving certain kinds of backward stochastic differential equations
- Numerical aspects of shot noise representation of infinitely divisible laws and related processes
- Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions
- DGM: a deep learning algorithm for solving partial differential equations
- An FBSDE approach to American option pricing with an interacting particle method
- Perturbative expansion technique for non-linear FBSDEs with interacting particle method
- Multistep schemes for forward backward stochastic differential equations with jumps
- High-order combined multi-step scheme for solving forward backward stochastic differential equations
- An efficient numerical method for forward-backward stochastic differential equations driven by \(G\)-Brownian motion
- Discretization and machine learning approximation of BSDEs with a constraint on the gains-process
- Donsker-type theorem for BSDEs: rate of convergence
- Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients
- Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
- Propagation of chaos: a review of models, methods and applications. II: Applications
- A fully quantization-based scheme for FBSDEs
- Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games. II: The finite horizon case
- Explicit multistep stochastic characteristic approximation methods for forward backward stochastic differential equations
- A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for deep BSDE solver
- Multistep schemes for solving backward stochastic differential equations on GPU
- Gradient boosting-based numerical methods for high-dimensional backward stochastic differential equations
- Existence and probabilistic representation of the solutions of semilinear parabolic PDEs with fractional Laplacians
- Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
- On the speed of convergence of Picard iterations of backward stochastic differential equations
- Numerical approximation of singular forward-backward SDEs
- Product Markovian quantization of a diffusion process with applications to finance
- An explicit second-order numerical scheme for mean-field forward backward stochastic differential equations
- Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method
- An efficient third-order scheme for BSDEs based on nonequidistant difference scheme
- A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
- Convergence of the deep BSDE method for coupled FBSDEs
- Mean field games and applications: numerical aspects
- Second-order schemes for solving decoupled forward backward stochastic differential equations
- Path regularity and explicit convergence rate for BSDE with truncated quadratic growth
- Random walk approximation of BSDEs with Hölder continuous terminal condition
- A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus
- On approximation of BSDE and multi-step MLE-processes
- A multi-step scheme based on cubic spline for solving backward stochastic differential equations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Explicit deferred correction methods for second-order forward backward stochastic differential equations
- On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
- Unnamed Item
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- Unnamed Item
- Unnamed Item
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- Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs
- Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
- A cubature based algorithm to solve decoupled McKean-Vlasov forward-backward stochastic differential equations
- A monotone scheme for high-dimensional fully nonlinear PDEs
- Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs
- Efficient spectral sparse grid approximations for solving multi-dimensional forward backward sdes
- Backward stochastic differential equations and applications to optimal control
- Reducing variance in the numerical solution of BSDEs
- Multi-dimensional BSDE with oblique reflection and optimal switching
- On the branching process for Brownian particles with an absorbing boundary
- Numerical method for FBSDEs of McKean-Vlasov type
- A Monte Carlo method for backward stochastic differential equations with Hermite martingales
- A numerical algorithm for a class of BSDEs via the branching process
- Stochastic differential equations, backward SDEs, partial differential equations
- Second order discretization of backward SDEs and simulation with the cubature method
- Runge-Kutta schemes for backward stochastic differential equations
- On approximation of the backward stochastic differential equation
- Simulation of BSDEs by Wiener chaos expansion
- A forward scheme for backward SDEs
- Discrete-time approximation of decoupled Forward-Backward SDE with jumps
- Time discretization and Markovian iteration for coupled FBSDEs
- Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
- Representations and regularities for solutions to BSDEs with reflections
- A forward-backward stochastic algorithm for quasi-linear PDEs
- Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions
- A decomposition approach for the discrete-time approximation of FBSDEs with a jump
- Discrete-time approximation for continuously and discretely reflected BSDEs
- Numerical methods for forward-backward stochastic differential equations
- Utility maximization in incomplete markets
- A regression-based Monte Carlo method to solve backward stochastic differential equations
- Error analysis of the optimal quantization algorithm for obstacle problems.
- BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations.
- Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by \(G\)-Brownian motion
- A Fourier transform method for solving backward stochastic differential equations
- Convergence of the deep BSDE method for FBSDEs with non-Lipschitz coefficients
- Quantitative stability and numerical analysis of Markovian quadratic BSDEs with reflection
- A multi-step algorithm for BSDEs based on a predictor-corrector scheme and least-squares Monte Carlo
- Numerical resolution of McKean-Vlasov FBSDEs using neural networks
- A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
- Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
- An overview on deep learning-based approximation methods for partial differential equations
- Pricing Via Utility Maximization and Entropy
- A stochastic quantization method for nonlinear problems
- Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions
- Short-time asymptotic expansions of semilinear evolution equations
- A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA
- The Forward-Backward Stochastic Heat Equation: Numerical Analysis and Simulation
- Stratified Regression Monte-Carlo Scheme for Semilinear PDEs and BSDEs with Large Scale Parallelization on GPUs
- Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations
- Discretization of backward stochastic Volterra integral equations
- Discrete-Time Approximation of Decoupled Forward‒Backward Stochastic Differential Equations Driven by Pure Jump Lévy Processes
- Discrete approximations of generalized RBSDE with random terminal time
- Monte-Carlo Valuation of American Options: Facts and New Algorithms to Improve Existing Methods
- Least-Squares Monte Carlo for Backward SDEs
- New Kinds of High-Order Multistep Schemes for Coupled Forward Backward Stochastic Differential Equations
- A Stable Multistep Scheme for Solving Backward Stochastic Differential Equations
- Results on Numerics for FBSDE with Drivers of Quadratic Growth
- Solving BSDE with Adaptive Control Variate
- SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION
- Numerical Method for Reflected Backward Stochastic Differential Equations
- Deferred Correction Methods for Forward Backward Stochastic Differential Equations
- ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDEs WITH PERTURBATION SCHEME
- Analytical Approximations of BSDEs with Nonsmooth Driver
- A General Stochastic Maximum Principle for Optimal Control Problems
- Discretization of forward–backward stochastic differential equations and related quasi-linear parabolic equations
- Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
- On Numerical Approximations of Forward-Backward Stochastic Differential Equations
- Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
- Backward Stochastic Differential Equations in Finance
- Recursive marginal quantization of higher-order schemes
- On the wavelet-based SWIFT method for backward stochastic differential equations
- An Efficient Gradient Projection Method for Stochastic Optimal Control Problems
- Optimal Error Estimates for a Fully Discrete Euler Scheme for Decoupled Forward Backward Stochastic Differential Equations
- Efficient Computation of Various Valuation Adjustments Under Local Lévy Models
- Arbitrage‐free XVA
- Nonlinear Monte Carlo Schemes for Counterparty Risk on Credit Derivatives
- Reflected BSDE's with discontinuous barrier and application
- Solving Backward Stochastic Differential Equations Using the Cubature Method: Application to Nonlinear Pricing
- A parallel algorithm for solving BSDEs
- Probabilistic methods for semilinear partial differential equations. Applications to finance
- Filtration stability of backward sde's
- Deep Splitting Method for Parabolic PDEs
- Deep backward schemes for high-dimensional nonlinear PDEs
- Cubature method to solve BSDEs: Error expansion and complexity control
- Solving high-dimensional partial differential equations using deep learning
- Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements
