  We address a class of backward stochastic differential equations on a bounded
interval, where the driving noise is a marked, or multivariate, point process.
Assuming that the jump times are totally inaccessible and a technical condition
holds (see Assumption (A) below), we prove existence and uniqueness results
under Lipschitz conditions on the coefficients. Some counter-examples show that
our assumptions are indeed needed. We use a novel approach that allows
reduction to a (finite or infinite) system of deterministic differential
equations, thus avoiding the use of martingale representation theorems and
allowing potential use of standard numerical methods. Finally, we apply the
main results to solve an optimal control problem for a marked point process,
formulated in a classical way.
