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Published online by Cambridge University Press:  10 July 2013

Erhan Bayraktar*
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109-1043, USA
Andreas E. Kyprianou
Department of Mathematical Sciences, The University of Bath, Claverton Down, Bath BA2 7AY, UK E-mail:
Kazutoshi Yamazaki
Department of Mathematics, Faculty of Engineering Science, Kansai University, Suita-shi, Osaka 564-8680, Japan E-mail:
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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.

Research Article
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Copyright © ASTIN Bulletin 2013


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