In this paper we study the one-dimensional reflected backward stochastic differential equations which are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. Using a penalization method, we prove the existence and uniqueness of the solutions to these equations. As an application, we show that under proper assumptions the solution of the reflected equation is the value of the related mixed optimal stopping-control problem.
Anticipated backward stochastic differential equation （ABSDE） studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for ABSDEs.
