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

TL;DR

This paper extends the theory of infinite horizon reflected backward stochastic differential equations to cases with stochastic Lipschitz coefficients, providing new insights for robust optimal stopping problems involving functional stochastic differential equations.

Contribution

It generalizes existing results on infinite horizon RBSDEs to include stochastic Lipschitz drivers, broadening their applicability in stochastic control.

Findings

Established existence and uniqueness of solutions under stochastic Lipschitz conditions.

Applied the theoretical results to robust optimal stopping problems for FSDEs.

Demonstrated the linear growth condition of the driver in the application.

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.