Optimal dividend and proportional reinsurance strategy for the risk model with common shock dependence

This article focuses on the classic optimal dividend and reinsurance problems. Different from the existing literature, it assumes that the insurance company has two lines of business with a common shock dependence. It can purchase proportional reinsurance to reduce business risk and pay dividends to stay competitive. The goal is to find out the optimal dividend and reinsurance strategies for maximizing the company's value. Under the diffusion approximation model, we decomposed the problem into several situations and gave the corresponding solutions by using the stochastic control method. Some numerical examples and economic explanations are presented to illustrate the results.