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We reconsider the study of optimal dividend strategies in theCram\'er-Lundberg risk model. It is well-known that the solution of theclassical dividend problem is in general a band strategy. However, thenumerical techniques for the identification of the optimal bands available inthe literature are very hard to implement and explicit numerical results areknown for very few cases only. In this paper we put a gradient-based methodinto place which allows to determine optimal bands in more general situations.In addition, we adapt an evolutionary algorithm to this dividend problem, whichis not as fast, but applicable in considerable generality, and can serve forproviding a competitive benchmark. We illustrate the proposed methods inconcrete examples, reproducing earlier results in the literature as well asestablishing new ones for claim size distributions that could not be studiedbefore.

Optimal dividends revisited: a gradient-based method and evolutionary algorithms