Quantization-based approximation of reflected BSDEs with extended upper bounds for recursive quantization

TL;DR

This paper develops new quantization error bounds for recursive schemes approximating reflected BSDEs, introducing a hybrid approach suitable for high-dimensional problems and providing numerical methods for solution computation.

Contribution

It introduces a hybrid recursive quantization scheme with extended bounds for high-dimensional reflected BSDEs and proposes a numerical approach for their solution.

Findings

Established upper bounds for $L^p$-quantization error in high dimensions.

Developed a hybrid recursive quantization scheme for easier implementation.

Provided numerical methods and error estimates for solving reflected BSDEs.

Abstract

We establish upper bounds for the $L^p$-quantization error, p in (1, 2+d), induced by the recursive Markovian quantization of a d-dimensional diffusion discretized via the Euler scheme. We introduce a hybrid recursive quantization scheme, easier to implement in the high-dimensional framework, and establish upper bounds to the corresponding $L^p$-quantization error. To take advantage of these extensions, we propose a time discretization scheme and a recursive quantization-based discretization scheme associated to a reflected Backward Stochastic Differential Equation and estimate $L^p$-error bounds induced by the space approximation. We will explain how to numerically compute the solution of the reflected BSDE relying on the recursive quantization and compare it to other types of quantization.