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

TL;DR

This paper introduces a gradient-based method and an evolutionary algorithm to identify optimal dividend strategies in the Cramér-Lundberg risk model, enabling analysis of more general cases and providing benchmarks.

Contribution

It presents a novel gradient-based approach and adapts an evolutionary algorithm for determining optimal dividend bands in complex scenarios.

Findings

The gradient-based method effectively finds optimal bands in general cases.

The evolutionary algorithm provides a flexible benchmark for the dividend problem.

New results for claim size distributions previously unexplored.

Abstract

We reconsider the study of optimal dividend strategies in the Cram\'er-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.