Under a competition between an insurance company and a reinsurance company, the formulation problem of the optimal reinsurance strategy is studied. There is an insurance company in the insurance market that operates $n$ kinds of dependent insurance businesses. For each insurance business, the insurance company reduces the claim risk by adopting proportional reinsurance. The insurance company and reinsurance company increase their wealth by investing in a common risk-free asset. Based on the relative performance, we quantify the competition between the insurance company and the reinsurance company, and derive the relative wealth process of the insurance company. Furthermore, we establish the stochastic optimization problem that the insurance company care about, i.e., find the optimal reinsurance strategy to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. Using stochastic calculus and stochastic control theory, we establish the extended Hamilton-Jacobi-Bellman (HJB) equation and verification theorem that the value function satisfies, and then using the stochastic optimization theory, we obtain the explicit solution of the optimal time-consistent reinsurance strategy and the corresponding optimal value function, and theoretically discuss the insurance and economic significance of the optimal reinsurance strategy. Furthermore, for the two insurance business case, the dependence of claim amounts and claim distributions are discussed, respectively, and the corresponding optimal reinsurance strategy is given. Finally, we analyze the influence of insurance business dependence, competition degree and the number of insurance businesses on the optimal time-consistent reinsurance strategy through numerical experiments. The research results can effectively guide the reinsurance practice of insurance companies.