BSDEs with polynomial growth generators in a defaultable market

In this paper we study a backward stochastic differential equation (BSDE for short) driven by a Brownian motion and a jump martingale in a defaultable setting, with a polynomial growth generator. This kind of BSDE has important applications to the defaultable market. To demonstrate this in a strict way, we first prove the existence, uniqueness and uniform p(p≥2) estimate of its solution. Then two examples are given to illustrate its applications to recursive utility and contingent claim hedging.