Dividend optimization under reserve constraints for the Cramér–Lundberg model compounded by force of interest

We study the dividend optimization problem for a company where surplus in the absence of dividend payments follows a Cramér–Lundberg process compounded by constant force of interest. The company controls the times and amounts of dividend payments subject to reserve constraints that dividends are not payable if the surplus is below b0 and that a dividend payment, if any, cannot reduce the surplus to a level below b0, and its objective is to maximize the expected total discounted dividends. We show how the optimality can be achieved under the constraints and construct an optimal strategy of a band type.