On optimal dividends in the dual model
Probability
2023-06-22 v3 Portfolio Management
Abstract
We revisit the dividend payment problem in the dual model of Avanzi et al. ([2], [1], and [3]). Using the fluctuation theory of spectrally positive L\'{e}vy processes, we give a short exposition in which we show the optimality of barrier strategies for all such L\'{e}vy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem of [3] and show that its value function has a very similar form to the one in which the horizon is the time of ruin.
Cite
@article{arxiv.1211.7365,
title = {On optimal dividends in the dual model},
author = {Erhan Bayraktar and Andreas Kyprianou and Kazutoshi Yamazaki},
journal= {arXiv preprint arXiv:1211.7365},
year = {2023}
}
Comments
To appear in the ASTIN Bulletin. Key words: dual model; dividends; capital injections; spectrally positive Levy processes; scale functions