Reinsurance and dividend policies for companies with debts

We consider a model of a financial corporation, which can choose a production/business policy among an available set of control policies with different expected profits and associated risks such as reinsurance for an insurance company. The risk the company takes also effects the potential profit it can receive. In addition the management of the company has to decide about the amount of dividends paid-out to the shareholders. Notwithstanding any policy decision there is a constant payment of a corporate debt, such as bond liability or loan amortization. The objective is to find the policy which maximizes the expected total discounted dividends pay-outs until the time of bankruptcy. We model the dynamics of the corporate assets as a diffusion process with controlled drift and with another additive type control, modeled by a general increasing process. This leads to a mixed regular-singular control problem for diffusion processes. We show find the optimal risk as a function of the current reserve (wealth) and the optimal level in excess of which the dividends should be paid out. We also establish the relation on the parameters of the model for which the company must take always the maximal risk