  This paper studies open-loop equilibriums for a general class of
time-inconsistent stochastic control problems under jump-diffusion SDEs with
deterministic coefficients. Inspired by the idea of Four-Step-Scheme for
forward-backward stochastic differential equations with jumps (FBSDEJs, for
short), we derive two systems of integro-partial differential equations (IPDEs,
for short). Then, we rigorously prove a verification theorem which provides a
sufficient condition for open-loop equilibrium strategies. As an illustration
of the general theory, we discuss a mean-variance portfolio selection problem
under a jump-diffusion model.
