Optimal proportional reinsurance and investment based on Hamilton–Jacobi–Bellman equation

In the whole paper, the claim process is assumed to follow a Brownian motion with drift and the insurer is allowed to invest in a risk-free asset and a risky asset. In addition, the insurer can purchase the proportional reinsurance to reduce the risk. The paper concerns the optimal problem of maximizing the utility of terminal wealth. By solving the corresponding Hamilton–Jacobi–Bellman equations, the optimal strategies about how to purchase the proportional reinsurance and how to invest in the risk-free asset and risky asset are derived respectively.