Sensitivity Analysis of Distributionally Robust BSDEs and RBSDEs

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 sensitivity analysis questions in distributionally robust optimization (DRO) control and optimal stopping problems, we establish explicit formulas for the corresponding sensitivities under drift perturbations of a reference measure. Our work is closely related to Bartl et al. In contrast to the existing literature, our analysis is carried out within a general non‐Markovian framework.