Optimal impulse stochastic control of the dividend for an insurance company with reinvestments

In this paper, we mainly studied the optimal problem of the insurance company with proportional reinsurance, dividend payment and capital injection policy under a diffusion risk model with capital injections. With each dividend payment there is a fixed and a proportional cost. And with each reinvestments, there´s a proportional cost. The goal is to maximize expected value of discounted net profit flow, i.e. dividends paid minus reinvestments. We solve this problem explicitly and construct the value function together with the optimal policy.