Well-posedness of a system of SDEs driven by jump random measures.

We establish well-posedness for a class of systems of SDEs with non-Lipschitz diffusion and jump terms, and with interdependence in monotone components of the drift terms and in the driving Brownian motions and jump random measures. We employ a comparison theorem to construct non-negative, $L^1$-integrable c\`adl\`ag solutions as monotone limits of solutions to approximating systems, allowing for time-inhomogeneous drift terms to be included, while the applicability of certain systems with time-homogeneous mean-field drift terms in financial modeling is also discussed. Finally, we implement a standard technique to prove that solutions are pathwise unique.