A Note on Reflected BSDEs in Infinite Horizon with Stochastic Lipschitz Coefficients

Abstract

We consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon reflected BSDEs to the setting where the driver has a stochastic Lipschitz coefficient. As an application we consider robust optimal stopping problems for functional stochastic differential equations (FSDEs) where the driver has linear growth.