On Reflected Bsdes With Jumps and Default Time

We introduce a new class of reflected BSDEs with default times and irregular obstacles, where the publicly available information is generated by a Brownian motion and an independent integer-valued random measure. Under a stochastic Lipschitz condition on the driver, we establish the well-posedness of the problem by proving the existence and uniqueness of a solution. As an application, we investigate the connection between these equations and optimal stopping problems with dynamic risk measures defined via nonlinear expectations, as well as the pricing and hedging of American options in a general defaultable market with jumps.