Optimal dividend control for a generalized risk model with investment incomes and debit interest

This paper investigates dividend optimization of an insurance corporation under a more realistic model which takes into consideration refinancing or capital injections. The model follows the compound Poisson framework with credit interest for positive reserve, and debit interest for negative reserve. Ruin occurs when the reserve drops below the critical value. The company controls the dividend pay-out dynamically with the objective to maximize the expected total discounted dividends until ruin. We show that that the optimal strategy is a band strategy and it is optimal to pay no dividends when the reserve is negative.