Quantitative stability and numerical analysis of Markovian quadratic BSDEs with reflection

TL;DR

This paper investigates the stability of solutions to Markovian quadratic reflected backward stochastic differential equations (BSDEs) with bounded terminal data and introduces a numerical scheme with explicit convergence rates.

Contribution

It provides new stability estimates using BMO martingale techniques and proposes a truncated discrete-time numerical scheme with proven convergence rates.

Findings

Stability estimates for solutions under different forward processes

A truncated numerical scheme with explicit convergence rate

Application of BMO martingale techniques in stability analysis

Abstract

We study the quantitative stability of the solutions to Markovian quadratic reflected BSDEs with bounded terminal data. By virtue of BMO martingale and change of measure techniques, we obtain stability estimates for the variation of the solutions with different underlying forward processes. In addition, we propose a truncated discrete-time numerical scheme for quadratic reflected BSDEs, and obtain the explicit rate of convergence by applying the quantitative stability result.