We reconsider the study of optimal dividend strategies in the Cramér-Lundberg risk model. It is well-known that the solution of the classical dividend problem is in general a band strategy. However, the numerical techniques for the identification of the optimal bands available in the literature are very hard to implement and explicit numerical results are known for very few cases only. In this paper we put a gradient-based method into place which allows to determine optimal bands in more general situations. In addition, we adapt an evolutionary algorithm to this dividend problem, which is not as fast, but applicable in considerable generality, and can serve for providing a competitive benchmark. We illustrate the proposed methods in concrete examples, reproducing earlier results in the literature as well as establishing new ones for claim size distributions that could not be studied before.

我们重新考虑 Cramér-Lundberg 风险模型中最优股息策略的研究。众所周知，经典股利问题的解决方案一般是波段策略。然而，文献中可用的用于识别最佳频带的数值技术很难实现，并且仅在极少数情况下才知道明确的数值结果。在本文中，我们采用了一种基于梯度的方法，可以在更一般的情况下确定最佳频段。此外，我们针对这个股利问题采用了进化算法，该算法虽然速度不快，但具有相当的通用性，可以为提供竞争基准。我们用具体的例子来说明所提出的方法，