Given p∈(1,2), we study Lp - solutions of a reflected backward stochastic differential equation with jumps (RBSDEJ) whose generator g is Lipschitz continuous in (y,z,u). We show that such a RBSDEJ with p - integrable parameters admits a unique Lp solution using a fixed-point argument as well...

Given p ∈ (1, 2), we study L^p solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in (y, z, u). We show that such a BSDEJ with a p−integrable terminal data admits a unique L^p solution by approximating...

The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the filtration of the underlying Brownian motion is proved. This result is applied to the pricing of contingent claims. It allows to compare the prices of agents who have different...