A primal-dual algorithm for BSDEs

Abstract

We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dynamic program, which was pre-computed, e.g., by least-squares Monte Carlo, our methodology allows to construct a confidence interval for the unknown true solution of the time discretized (reflected) BSDE at time 0. We numerically demonstrate the practical applicability of our method in two five-dimensional nonlinear pricing problems where tight price bounds were previously unavailable.

References in corpus (2)

• Numerical simulation of quadratic BSDEs
• Solving optimal stopping problems via empirical dual optimization

Cited by in corpus (10)

• Solving high-dimensional partial differential equations using deep learning
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and 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
• 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
• Solving high-dimensional optimal stopping problems using deep learning
• Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
• Numerical methods for backward stochastic differential equations: A survey
• On existence and uniqueness properties for solutions of stochastic fixed point equations