A regression-based Monte Carlo method to solve backward stochastic differential equations

Abstract

We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo simulations. A full convergence analysis is derived. Numerical experiments about finance are included, in particular, concerning option pricing with differential interest rates.

Published at http://dx.doi.org/10.1214/105051605000000412 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• A regression-based Monte Carlo method to solve backward stochastic differential equations
• Hedged Monte-Carlo: low variance derivative pricing with objective probabilities

Cited by in corpus (79)

• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• A regression-based Monte Carlo method to solve backward stochastic differential equations
• Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
• Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
• A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
• On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
• Deep splitting method for parabolic PDEs
• On some recent aspects of stochastic control and their applications
• An overview on deep learning-based approximation methods for partial differential equations
• Time discretization and Markovian iteration for coupled FBSDEs
• Simulation of BSDEs by Wiener chaos expansion
• Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
• Path regularity and explicit convergence rate for BSDE with truncated quadratic growth
• Solving high-dimensional optimal stopping problems using deep learning
• Numerical simulation of quadratic BSDEs
• A monotone scheme for high-dimensional fully nonlinear PDEs
• Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs
• Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
• Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
• Malliavin calculus for backward stochastic differential equations and application to numerical solutions
• Runge-Kutta schemes for backward stochastic differential equations
• A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation
• Numerical methods for backward stochastic differential equations: A survey
• Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs
• BSΔEs and BSDEs with non-Lipschitz drivers: Comparison, convergence and robustness
• Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
• Discrete-time approximation of multidimensional BSDEs with oblique reflections
• Variational approach to rare event simulation using least-squares regression
• On the homotopy analysis method for backward/forward-backward stochastic differential equations
• Neural networks-based algorithms for stochastic control and PDEs in finance
• BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula
• Generalised multilevel Picard approximations
• A Hedged Monte Carlo Approach to Real Option Pricing
• Regress-Later Monte Carlo for optimal control of Markov processes
• On the wavelets-based SWIFT method for backward stochastic differential equations
• Second-order numerical schemes for decoupled forward-backward stochastic differential equations with jumps
• Stochastic grid bundling method for backward stochastic differential equations
• Deep backward schemes for high-dimensional nonlinear PDEs
• Numerical Methods and Analysis via Random Field Based Malliavin Calculus for Backward Stochastic PDEs
• Weak approximation of second-order BSDEs
• Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations
• Convergence Error Estimates of the Crank-Nicolson Scheme for Solving Decoupled FBSDEs
• A convolution method for numerical solution of backward stochastic differential equations
• Quasi-Regression Monte-Carlo scheme for semi-linear PDEs and BSDEs with large scale parallelization on GPUs
• Second order discretization of Backward SDEs
• Multistep schemes for solving backward stochastic differential equations on GPU
• A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential Equations
• A Finite Horizon Optimal Multiple Switching Problem
• Exploration noise for learning linear-quadratic mean field games
• Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise
• On the convergence of monotone schemes for path-dependent PDE
• Approximations for adapted M-solutions of Type-II backward stochastic Volterra integral equations
• Generalized fractional smoothness and $L_p$-variation of BSDEs with non-Lipschitz terminal condition
• Strong Rates of Convergence for Space-Time Discretization of the Backward Stochastic Heat Equation, and of a Linear-Quadratic Control Problem for the Stochastic Heat Equation
• Numerical approximation of BSDEs using local polynomial drivers and branching processes
• A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation
• Solvability of one kind of forward-backward stochastic difference equations
• Novel multi-step predictor-corrector schemes for backward stochastic differential equations
• Numerical analysis of a Neumann boundary control problem with a stochastic parabolic equation
• Numerical approximation of singular Forward-Backward SDEs
• On the discretization of backward doubly stochastic differential equations
• Numerical method for hyperbolic conservation laws via forward backward SDEs
• A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs
• A regression Monte-Carlo method for Backward Doubly Stochastic Differential Equations
• Solvability of finite state forward-backward stochastic difference equations
• Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition
• On the parabolic equation for portfolio problems
• A decomposition approach for the discrete-time approximation of FBSDEs with a jump I : the Lipschitz case
• A Semidiscrete Galerkin Scheme for Backward Stochastic Parabolic Differential Equations
• Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models
• A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing
• Impulse Control of a Diffusion with a Change Point
• Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme
• Deep Operator BSDE: a Numerical Scheme to Approximate Solution Operators
• A decomposition approach for the discrete-time approximation of BSDEs with a jump II: the quadratic case
• Pathwise Iteration for Backward SDEs
• Error expansion for the discretization of Backward Stochastic Differential Equations
• Swing Options Valuation: a BSDE with Constrained Jumps Approach
• High-order combined Multi-step Scheme for solving forward Backward Stochastic Differential Equations