Optimal dividend and equity issuance in the perturbed dual model under a penalty for ruin.

In this paper, we consider the dividends and equity issuances control problem in the perturbed dual model under a penalty for ruin. Transaction costs are incurred by these business activities: dividend is taxed and fixed costs are generated by equity issuance. The objective is to maximize the expected present value of dividends minus the discounted costs of equity issuances and the discounted penalty until the ruin time. We find the joint optimal dividend and equity issuance strategy by solving the control problems of two categories of suboptimal model. Furthermore, we derive the explicit closed solutions for the value functions and the optimal strategies when the jumps are mixed exponential. In particular, we investigate the effects of the penalty, the proportional and fixed transaction costs, the expense rate and the force of interest on the optimal strategies by numerical calculations, and give some interesting economic insights. [ABSTRACT FROM AUTHOR]