  In this paper we are concerned with backward stochastic differential
equations with random default time and their applications to default risk. The
equations are driven by Brownian motion as well as a mutually independent
martingale appearing in a defaultable setting. We show that these equations
have unique solutions and a comparison theorem for their solutions. As an
application, we get a saddle-point strategy for the related zero-sum stochastic
differential game problem.
