Sensitivity Analysis of Distributionally Robust BSDEs and RBSDEs

TL;DR

This paper investigates how distributionally robust backward stochastic differential equations and reflected BSDEs respond to parameter changes, providing explicit sensitivity formulas within a broad non-Markovian setting.

Contribution

It introduces explicit sensitivity formulas for DRBSDEs and RBSDEs under drift uncertainty, extending analysis to a general non-Markovian framework.

Findings

Derived explicit sensitivity formulas for DRBSDEs and RBSDEs.

Extended sensitivity analysis to non-Markovian settings.

Related work by Bartl et al. is closely connected.

Abstract

We examine the sensitivity properties of backward stochastic differential equations and reflected backward stochastic differential equations, which naturally arise in the context of optimal control and optimal stopping problems. Motivated by issues of sensitivity analysis in distributionally robust optimization (DRO) control and optimal stopping problems, we establish explicit formulas for the corresponding sensitivities under drift reference measure uncertainty. Our work is closely related to \citeauthor{bartl2023sensitivity} \cite{bartl2023sensitivity}. In contrast to the existing literature, our analysis is carried out within a general non-Markovian framework.