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arXiv · 1211.7365

On optimal dividends in the dual model

Erhan Bayraktar·Andreas Kyprianou·Kazutoshi Yamazaki
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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.

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Erhan Bayraktar, Andreas Kyprianou, Kazutoshi Yamazaki. 2012-11-30. On optimal dividends in the dual model. https://doi.org/10.1017/asb.2013.17

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