Optimal dividend and capital injection of the insurance company with proportional reinsurance policy

This paper deals with the optimal control problem of the insurance company with proportional reinsurance policy. By controlling the dynamic reinsurance rate, dividends payout as well as the equity issuance processes, we maximize the cumulative expected discounted dividends payout minus the equity issuance. Moreover, we prove that it is optimal to issue new equity when the process hits 0.