A large number of empirical studies have shown that future claims are correlated with historical claims. Based on the extrapolation method, this paper establishes the dependence of future claims on historical claims, presents the premium calculation method, and then establishes the surplus process of insurance company. In order to avoid the claim risks, reinsurance is considered; in order to increase wealth, investment in financial market is considered. Therefore, the optimal decision-marking of the insurance company includes the optimal decision-marking of reinsurance and the optimal decision-marking of investment. We establish the Hamilton-Jacobi-Bellman (HJB) equation of the value function and verification theorem by using stochastic control theory. Then, under the expected utility framework, the optimal reinsurance and investment strategies are derived. Meanwhile, the investment criteria of centralization and decentralization of the insurance company are obtained. Finally, the influence of the key parameters of the model on the optimal reinsurance and investment strategy is analyzed in detail in both theoretical and numerical experiments, and some profound decision-making suggestions are obtained.