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

Optimality of Excess-Loss Reinsurance under a Mean-Variance Criterion