Time discretization and Markovian iteration for coupled FBSDEs

TL;DR

This paper introduces a novel numerical algorithm for simulating high-dimensional coupled FBSDEs, proving convergence of a new time discretization and Markovian iteration that maintains fixed process dimension, enabling efficient high-dimensional simulations.

Contribution

It develops a convergence-proof for a new time discretization and Markovian iteration method that keeps the process dimension fixed, improving efficiency for high-dimensional FBSDEs.

Findings

Proved convergence of the proposed discretization and iteration methods.

Developed a fully explicit numerical algorithm.

Demonstrated effectiveness with numerical examples up to 10 dimensions.

Abstract

In this paper we lay the foundation for a numerical algorithm to simulate high-dimensional coupled FBSDEs under weak coupling or monotonicity conditions. In particular, we prove convergence of a time discretization and a Markovian iteration. The iteration differs from standard Picard iterations for FBSDEs in that the dimension of the underlying Markovian process does not increase with the number of iterations. This feature seems to be indispensable for an efficient iterative scheme from a numerical point of view. We finally suggest a fully explicit numerical algorithm and present some numerical examples with up to 10-dimensional state space.