Existence and uniqueness for BSDEs driven by a general random measure, possibly non quasi-left-continuous

We study the following backward stochastic differential equation on finite time horizon driven by an integer-valued random measure ц on R+ × E, where E is a Lusin space, with compensator v(dt, dx) = dAt Øt(dx): The generator f satisfies, as usual, a uniform Lipschitz condition with respect to its last two arguments. In the literature, the existence and uniqueness for the above equation in the present general setting has only been established when A is continuous or deterministic. The general case, i.e. A is a right-continuous nondecreasing predictable process, is addressed in this paper.