We establish well-posedness for a class of systems of SDEs with non-Lipschitz coefficients in the diffusion and jump terms and with two sources of interdependence: a monotone function of all the components in the drift of each SDE and the correlation between the driving Brownian motions and jump random measures. Pathwise uniqueness is derived by employing some standard techniques. Then, we use a comparison theorem along with our uniqueness result to construct non-negative, $L^1$-integrable càdlàg solutions as monotone limits of solutions to approximating SDEs, allowing for time-inhomogeneous drift terms to be included. Our approach allows also for a comparison property to be established for the solutions to the systems we investigate. The applicability of certain systems in financial modeling is also discussed.

我们为一类 SDE 系统建立了适定性，该系统在扩散项和跳跃项中具有非 Lipschitz 系数，并且具有两个相互依赖源：每个 SDE 漂移中所有分量的单调函数以及驱动布朗函数之间的相关性运动和跳跃随机措施。路径独特性是通过采用一些标准技术得出的。然后，我们使用比较定理以及我们的唯一性结果来构造非负，$L^1$-可积 càdlàg 解作为近似 SDE 解的单调极限，允许包含时间不均匀漂移项。我们的方法还可以为我们研究的系统的解决方案建立比较属性。还讨论了某些系统在财务建模中的适用性。