Optimal Dividend and Financing Control Problem in the Risk Model with Non-Cheap Proportional Reinsurance

In this paper, we consider the optimal dividend and financing control problem in the risk model with non-cheap proportional reinsurance and two kinds of transaction costs. The company control its reserves by paying dividends, issuing equity and taking reinsurance. In our model, the objective is to find the strategy which maximizes the expected present value of the dividends payout minus the equity issuance until the time of ruin. We solve the optimal control problem and identify the optimal strategy by constructing two categories of suboptimal control problems, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance.