As a part of a course, we have studied the paper by D. Higham and P. Kloeden "Numerical methods for nonlinear stochastic differential equations with jumps" where they discuss stability properties for nonlinear SDEs with jumps. However, in the example section, they only test their observations against the Merton model, which is linear.
Thus my question is can you point me toward a nonlinear SDE with jumps, which still satisfies the Lipschitz conditions (can be multi-dimensional)?
I am aware that I could simply construct it myself, but it would be better if I would have a reference. The only nonlinear SDE I have had luck with finding was the Heston model, but it is well known that it is not Lipschitz.