  In this paper, we study an insurer's reinsurance-investment problem under a
mean-variance criterion. We show that excess-loss is the unique equilibrium
reinsurance strategy under a spectrally negative L\'{e}vy insurance model when
the reinsurance premium is computed according to the expected value premium
principle. Furthermore, we obtain the explicit equilibrium
reinsurance-investment strategy by solving the extended Hamilton-Jacobi-Bellman
equation.
