A Fully Quantization-based Scheme for FBSDEs

TL;DR

This paper introduces a fully quantization-based numerical scheme for solving decoupled FBSDEs, eliminating the need for Monte Carlo simulations and demonstrating high effectiveness in financial applications.

Contribution

The paper simplifies existing quantization schemes for FBSDEs, making them fully recursive and Monte Carlo-free, with detailed error analysis and practical financial application demonstrations.

Findings

Scheme is fully based on recursive marginal quantization

Eliminates Monte Carlo simulation for conditional expectations

Proves effective in financial applications

Abstract

We propose a quantization-based numerical scheme for a family of decoupled FBSDEs. We simplify the scheme for the control in Pag\`es and Sagna (2018) so that our approach is fully based on recursive marginal quantization and does not involve any Monte Carlo simulation for the computation of conditional expectations. We analyse in detail the numerical error of our scheme and we show through some examples the performance of the whole procedure, which proves to be very effective in view of financial applications.