ON OPTIMAL DIVIDENDS IN THE DUAL MODEL

Erhan Bayraktar, Andreas E. Kyprianou and Kazutoshi Yamazaki

ASTIN Bulletin, 2013, vol. 43, issue 3, 359-372

Abstract: We revisit the dividend payment problem in the dual model of Avanzi et al. ([2–4]). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem of [4] and show that its value function has a very similar form to the one in which the horizon is the time of ruin.

Date: 2013
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