The existing literature on investment and reinsurance is limited to the study of continuous-time problems, while discrete-time problems are always ignored by re-searchers. In this study, we first discuss a multi-period investment and reinsurance opti-mization problem under the classical mean-variance framework. When the asset retus with a serially correlated structure, the time-consistent investment and reinsurance strategies are acquired via backward induction. In addition, we propose an alteative time-consistent mean-variance optimization model that contrasts with the classical mean-variance model, and the corresponding optimal strategy and value function are also derived. We find that the investment and reinsurance strategies are both independent of the current wealth for the above two optimization problems, which coincides with the conclusion presented in the continuous-time problems. Most importantly, the above in-vestment strategies with serially correlated structures are both conditional mean-based strategies, rather than unconditional ones. Finally, we compare the investment and rein-surance strategies suggested above based on the simulation approach, to shed light on which investment-reinsurance strategies are more suitable for insurers.