Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities

TL;DR

This paper extends the analysis of hybrid dividend strategies to a dual spectrally positive Lévy process, demonstrating their optimality and providing explicit expressions using scale functions, supported by numerical validation.

Contribution

It generalizes previous results from Brownian models to spectrally positive Lévy models, establishing the optimality of hybrid barrier strategies and deriving explicit formulas.

Findings

Hybrid barrier strategies are optimal in the dual Lévy model.

Explicit expressions for strategies are derived using scale functions.

Numerical experiments confirm theoretical results.

Abstract

Avanzi et al. (2016) recently studied an optimal dividend problem where dividends are paid both periodically and continuously with different transaction costs. In the Brownian model with Poissonian periodic dividend payment opportunities, they showed that the optimal strategy is either of the pure-continuous, pure-periodic, or hybrid-barrier type. In this paper, we generalize the results of their previous study to the dual (spectrally positive L\'evy) model. The optimal strategy is again of the hybrid-barrier type and can be concisely expressed using the scale function. These results are confirmed through a sequence of numerical experiments.