  In this paper, we consider the classical problem of utility maximization in a
financial market allowing jumps. Assuming that the constraint set is a compact
set, rather than a convex one, we use a dynamic method from which we derive a
specific BSDE. We then aim at showing existence and uniqueness results for the
introduced BSDE. This allows us to give an explicit expression of the value
function and characterize optimal strategies for our problem.
