As classical mean-variance preferences have the shortcoming of
non-monotonicity, portfolio selection theory based on monotone mean-variance
preferences is becoming an important research topic recently. In
continuous-time Cram\'er-Lundberg insurance and Black-Scholes financial market
model, we solve the optimal reinsurance-investment strategies of insurers under
mean-variance preferences and monotone mean-variance preferences by the HJB
equation and the HJBI equation, respectively. We prove the validity of
verification theorems and find that the optimal strategies under the two
preferences are the same. This illustrates that neither the continuity nor the
completeness of the market is necessary for the consistency of two optimal
strategies. We make detailed explanations for this result. Thus, we develop the
existing theory of portfolio selection problems under the monotone
mean-variance criterion